Finite Group DatabasebetaFinite Group Databasebeta| order | 28086 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C151 ⋊ C2×C3 |
| Hall | #28380581 ⋊ C2 |
| Hall | D4681 ⋊ C3 |
| Sylow | C151 ⋊ D31⋊C3 |
| Sylow | C31 ⋊ D151⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C151 | C2×C3 |
| LCS | G ▷ C31×C151 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 182 |
| transitive degree | μt(G) = 4681 |
A minimal faithful permutation representation — 2 generators on 182 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)(82,129,130,103,104,158)(84,127,128,106,102,121)(87,96,126,108,109,122)(91,142,143,114,115,117)(94,147,140,118,119,112)(105,162,163,132,133,181)(107,161,134,135,131,155)(110,125,160,137,138,156)(116,171,168,144,145,151)(120,174,172,148,149,146)(123,176,169,152,153,141)(136,182,166,165,164,179)(139,159,175,167,150,180)(154,178,170,157,177,173);(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)(32,33,36,42,50,63,82,105,134,101,126,147,142,127,100,125,157,152,109,62,79,90,93,95,121,151,167,137,108,85,66,53,38,37,43,52,65,84,107,136,166,130,160,176,174,171,161,129,159,148,118,86,49,60,70,72,92,117,146,173,169,140,111,76,46,57,45,56,71,91,116,133,164,163,175,177,178,180,181,182,162,144,114,89,67,41,47,55,69,88,112,141,170,172,143,99,59,74,75,58,73,94,120,150,104,131,145,149,153,156,158,179,165,135,106,83,64,51,35,39,44,54,68,87,110,139,168,128,78,97,113,98,77,96,123,154,138,81,102,115,119,122,124,155,132,103,80,61,48,40,34)Polycyclic presentation:
2,3,31,151|c^a=c^30,d^a=d^150,c^b=c^25,d^b=d^118786 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28086, 24);