Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C23 |
| direct product | C71×#12955 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #442 |
| commutator | C2×C8 | C22×C4×C71 |
| Frattini, cosocle | C22×C8 | C23×C71 |
| prime radical | C2×#135×C71 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C22×C4×C71 ◁ C2×#97×C71 ◁ G | |
408 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)(6,12,13,19)(7,15,16,14)(8,17)(9,18)(10,20)(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);(2,4)(5,6,10,15,11,13,20,14)(7,9,19,8,16,17,12,18);(5,7)(6,9)(8,15)(10,19)(11,16)(12,20)(13,17)(14,18)2840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 5943);