Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C26 |
| direct product | C71×#24438 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C71 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C71 ◁ C2×C4×D4×C71 ◁ G | |
1498 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 4 generators on 95 points:
(1,2,3,4)(9,10,14,19)(11,20,12,16)(13,17,23,18)(15,22,24,21)(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);(5,6)(7,8)(9,11,14,12)(10,15,19,24)(13,22,23,21)(16,17,20,18);(2,4)(6,8)(9,12,14,11)(10,16,19,20)(13,22,23,21)(15,17,24,18);(10,17)(13,23)(15,20)(16,24)(18,19)(21,22)3692 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 17426);