Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C71 · Schur multiplier (H2) = C2×C43 |
| direct product | C4×H(3,ℤ/4)×C71 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C71 | C42 |
| commutator | C4 | C43×C71 |
| Frattini, cosocle | C23×C4 | C23×C71 |
| socle | C22×C71 | C2×#95 |
| prime radical | C24×C71 | C2×D4 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C42×C71 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(5,6)(7,13,15,19)(8,11)(9,12)(10,14,17,20)(16,18);(5,7)(6,10,12,17)(8,14)(9,15)(11,13,18,19)(16,20)6248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 3685);