Finite Group DatabasebetaFinite Group Databasebeta| order | 24402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C83⋊(D49⋊C3) |
| unambiguous semidirect product | (C49⋊C3)⋊D83 |
| unambiguous semidirect product | D4067⋊C3 |
| Fitting, derived, Hall | C49×C83 ⋊ C2×C3 |
| Hall | C83×C49⋊C3 ⋊ C2 |
| Hall | D4067 ⋊ C3 |
| Hall | C49⋊C3 ⋊ D83 |
| Sylow | C83 ⋊ D49⋊C3 |
| Sylow | C49 ⋊ C3×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C83 | C2×C3 |
| Frattini | C7 | ΓL(1,𝔽8)⋊D83 |
| socle | C7×C83 | AGL(1,𝔽7) |
| LCS | G ▷ C49×C83 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 132 |
| transitive degree | μt(G) = 4067 |
A minimal faithful permutation representation — 2 generators on 132 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)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(85,93,95,87,88,96)(86,105,107,91,92,108)(89,117,104,98,99,126)(90,122,123,102,103,132)(94,101,100,106,111,119)(97,120,129,115,116,130)(109,121,124,127,110,113)(112,125,114,128,118,131);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(84,106,103,114,113,118,87,91,128,97,96,123,98,102,105,129,88,117,119,111,126,107,127,121,120,116,110,109,108,104,101,100,99,93,130,92,90,89,132,95,115,112,86,85,125,124,131,122,94)Polycyclic presentation:
2,3,7,83,7|c^7=e^6,c^a=c^6e,d^a=d^82,e^a=e^6,c^b=c^2e^3,e^b=e^2793 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24402, 12);