Finite Group DatabasebetaFinite Group Databasebeta| order | 35898 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C193 ⋊ C2×C3 |
| Hall | #31822686 ⋊ C2 |
| Hall | D5983 ⋊ C3 |
| Sylow | C193 ⋊ D31⋊C3 |
| Sylow | C31 ⋊ D193⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C193 | C2×C3 |
| LCS | G ▷ C31×C193 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 224 |
| transitive degree | μt(G) = 5983 |
A minimal faithful permutation representation — 2 generators on 224 points:
(2,6,7,3,4,8)(5,14,15,9,10,22)(11,24,25,17,18,30)(12,23,19,20,16,13)(21,31,28,27,26,29)(33,37,38,34,35,39)(36,45,46,40,41,55)(42,58,59,48,49,72)(43,57,53,51,47,44)(50,77,78,61,62,95)(52,75,76,64,60,69)(54,56,74,66,67,70)(63,100,101,80,81,124)(65,98,99,83,79,92)(68,73,97,85,86,93)(71,113,111,89,90,88)(82,129,130,103,104,159)(84,127,128,106,102,121)(87,96,126,108,109,122)(91,142,143,114,115,117)(94,148,140,118,119,112)(105,164,165,132,133,198)(107,162,163,135,131,156)(110,125,161,137,138,157)(116,175,176,144,145,152)(120,182,180,149,150,147)(123,187,173,153,154,141)(134,203,204,167,168,224)(136,201,202,169,166,195)(139,160,200,170,171,196)(146,208,209,177,178,191)(151,213,214,183,184,186)(155,217,211,188,189,181)(158,220,206,192,193,174)(172,199,210,205,179,223)(185,222,207,197,215,219)(190,221,212,194,218,216);(1,2,5,11,19,7,6,12,21,28,15,23,14,18,26,25,30,31,24,10,16,22,29,27,20,4,8,13,17,9,3)(32,33,36,42,50,63,82,105,134,165,200,220,217,213,208,201,164,199,177,144,114,89,67,41,47,55,69,88,112,141,174,207,209,163,101,126,148,142,127,100,125,158,194,188,153,109,62,79,90,93,95,121,152,186,216,211,180,143,99,59,74,75,58,73,94,120,151,185,171,104,131,145,150,154,157,159,195,205,170,137,108,85,66,53,38,37,43,52,65,84,107,136,168,204,210,215,218,221,222,223,224,203,169,135,106,83,64,51,35,39,44,54,68,87,110,139,172,202,130,161,187,182,175,162,129,160,197,183,149,118,86,49,60,70,72,92,117,147,181,212,214,176,128,78,97,113,98,77,96,123,155,190,192,138,81,102,115,119,122,124,156,191,219,206,173,140,111,76,46,57,45,56,71,91,116,146,179,133,166,178,184,189,193,196,198,167,132,103,80,61,48,40,34)Polycyclic presentation:
2,3,31,193|c^a=c^30,d^a=d^192,c^b=c^25,d^b=d^1081003 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35898, 24);