Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C71 · Schur multiplier (H2) = C22 |
| direct product | C71×#10556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C71 |
| prime radical | C23×C71 | #124 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
364 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 3 generators on 95 points:
(1,2,5,3)(4,6,8,7)(9,10,14,18)(11,19,20,23)(12,15,13,17)(16,21,24,22)(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);(1,3,5,2)(4,7,8,6)(10,15)(11,20)(12,13)(16,19)(17,18)(23,24);(2,6)(3,7)(4,8)(9,11,12,21,14,20,13,22)(10,16,17,23,18,24,15,19)2627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 3544);