Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C24 |
| direct product | C71×#8402 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C71 | #120 |
| commutator | C22×C4 | C22×C4×C71 |
| Frattini, cosocle | C2×C42 | C23×C71 |
| socle | C22×C71 | #379 |
| prime radical | #537×C71 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C71 ◁ C2×C42×C71 ◁ G | |
716 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 3 generators on 95 points:
(2,5,6,7)(9,10,13,17,14,11,18,16)(12,15,20,24,21,19,22,23)(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);(1,2)(3,7)(4,6)(5,8)(9,11)(10,14)(12,19)(13,16)(15,21)(17,18)(20,23)(22,24);(9,12,14,21)(10,15,11,19)(13,22,18,20)(16,24,17,23)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 1390);