Finite Group DatabasebetaFinite Group Databasebeta| order | 33582 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊(D193⋊C3) |
| unambiguous semidirect product | (C193⋊C3)⋊D29 |
| unambiguous semidirect product | D5597⋊C3 |
| Fitting, socle, derived, Hall | C29×C193 ⋊ C2×C3 |
| Hall | C29×C193⋊C3 ⋊ C2 |
| Hall | D5597 ⋊ C3 |
| Hall | C193⋊C3 ⋊ D29 |
| Sylow | C193 ⋊ C3×D29 |
| Sylow | C29 ⋊ D193⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C193 | C2×C3 |
| LCS | G ▷ C29×C193 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 222 |
| transitive degree | μt(G) = 5597 |
A minimal faithful permutation representation — 2 generators on 222 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(31,35,36,32,33,37)(34,43,44,38,39,53)(40,56,57,46,47,70)(41,55,51,49,45,42)(48,75,76,59,60,93)(50,73,74,62,58,67)(52,54,72,64,65,68)(61,98,99,78,79,122)(63,96,97,81,77,90)(66,71,95,83,84,91)(69,111,109,87,88,86)(80,127,128,101,102,157)(82,125,126,104,100,119)(85,94,124,106,107,120)(89,140,141,112,113,115)(92,146,138,116,117,110)(103,162,163,130,131,197)(105,160,161,133,129,154)(108,123,159,135,136,155)(114,174,175,142,143,150)(118,181,179,147,148,145)(121,186,172,151,152,139)(132,201,171,165,166,203)(134,199,200,167,164,194)(137,158,198,169,170,195)(144,206,207,176,177,190)(149,211,212,182,183,185)(153,215,209,187,188,180)(156,218,204,191,192,173)(168,221,205,196,202,222)(178,219,210,193,208,220)(184,216,214,189,213,217);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(30,31,34,40,48,61,80,103,132,131,164,177,183,188,192,195,197,222,204,172,138,109,74,44,55,43,54,69,89,114,144,178,191,136,79,100,113,117,120,122,154,190,217,212,175,126,76,95,111,96,75,94,121,153,189,182,147,116,84,47,58,68,70,90,115,145,180,210,200,128,159,186,181,174,160,127,158,196,167,133,104,81,62,49,33,37,42,52,66,85,108,137,171,166,202,208,213,216,219,221,201,203,169,135,106,83,64,51,36,35,41,50,63,82,105,134,168,170,102,129,143,148,152,155,157,194,220,209,179,141,97,57,72,73,56,71,92,118,149,184,187,151,107,60,77,88,91,93,119,150,185,214,207,161,99,124,146,140,125,98,123,156,193,176,142,112,87,65,39,45,53,67,86,110,139,173,205,163,198,218,215,211,206,199,162,165,130,101,78,59,46,38,32)Polycyclic presentation:
2,3,29,193|c^a=c^28,d^a=d^192,d^b=d^84976 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33582, 12);