Finite Group DatabasebetaFinite Group Databasebeta| order | 33666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C181 ⋊ C2×C3 |
| Hall | #30682779 ⋊ C2 |
| Hall | D5611 ⋊ C3 |
| Sylow | C181 ⋊ D31⋊C3 |
| Sylow | C31 ⋊ D181⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C181 | C2×C3 |
| LCS | G ▷ C31×C181 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 212 |
| transitive degree | μt(G) = 5611 |
A minimal faithful permutation representation — 2 generators on 212 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)(105,164,165,132,133,194)(107,162,163,135,131,156)(110,125,161,137,138,157)(116,176,168,144,145,152)(120,182,180,149,150,147)(123,186,174,153,154,141)(134,183,184,167,151,205)(136,196,197,169,166,192)(139,160,195,171,172,193)(146,201,199,177,178,189)(155,208,173,187,188,181)(158,209,200,190,191,175)(170,206,207,198,185,211)(179,212,204,202,203,210);(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)(32,33,36,42,50,63,82,105,134,168,128,78,97,113,98,77,96,123,155,133,166,178,184,188,191,193,194,211,212,206,183,149,118,86,49,60,70,72,92,117,147,181,171,137,108,85,66,53,38,37,43,52,65,84,107,136,170,199,163,101,126,148,142,127,100,125,158,172,104,131,145,150,154,157,159,192,210,202,177,144,114,89,67,41,47,55,69,88,112,141,175,200,174,140,111,76,46,57,45,56,71,91,116,146,179,204,197,130,161,186,182,176,162,129,160,190,138,81,102,115,119,122,124,156,189,198,169,135,106,83,64,51,35,39,44,54,68,87,110,139,173,180,143,99,59,74,75,58,73,94,120,151,185,203,207,165,195,209,208,205,201,196,164,187,153,109,62,79,90,93,95,121,152,167,132,103,80,61,48,40,34)Polycyclic presentation:
2,3,31,181|c^a=c^30,d^a=d^180,c^b=c^25,d^b=d^132941 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33666, 24);