Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#23191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C71 | C22×D4 |
| commutator | C2×C4 | C23×C4×C71 |
| Frattini, cosocle | C22×C4 | C24×C71 |
| prime radical | C22×D8×C71 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C71 ◁ C4×C4⋊C4×C71 ◁ G | |
1026 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 4 generators on 95 points:
(2,4)(5,6,8,7)(9,10,14,15,13,16,12,18)(11,19,22,24,21,17,20,23)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(5,7,8,6)(10,15)(11,20)(12,14)(16,18)(21,22)(23,24);(1,2,3,4)(10,16)(15,18)(17,19)(23,24);(9,11,14,22,13,21,12,20)(10,17,15,23,16,19,18,24)4118 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 16179);