Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C24 |
| direct product | C71×#23716 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C71 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| socle | C22×C71 | C2×#121 |
| prime radical | C71×#2018 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C71 ◁ C2×C42×C71 ◁ G | |
816 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 4 generators on 95 points:
(1,2)(3,6)(4,5)(7,8)(9,10,12,16,13,17,21,15)(11,14,18,22,20,24,19,23)(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);(2,5)(6,8)(9,11)(10,14)(12,18)(13,20)(15,23)(16,22)(17,24)(19,21);(10,15)(11,18)(12,21)(16,17)(19,20)(22,23);(1,3,4,7)(2,6,5,8)3692 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 16704);