Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C24 |
| direct product | C71×#19396 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C71 |
| prime radical | C2×#127×C71 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 4 generators on 95 points:
(2,5)(3,7)(6,8)(11,17)(12,19)(14,21)(16,23)(18,20)(22,24)(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);(1,2,3,5,4,6,7,8)(9,10)(11,14)(12,16)(13,15)(17,21)(18,22)(19,23)(20,24);(9,11,13,18)(10,14,15,22)(12,20,19,17)(16,24,23,21);(10,15)(14,22)(16,23)(21,24)3479 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 12384);