Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#12767 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C71 | #1790 |
| commutator | C2×D4 | C22×C4×C71 |
| Frattini, cosocle | C22×D4 | C23×C71 |
| prime radical | C71×#3543 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C71 ◁ C23×C71 ◁ C22×D4×C71 ◁ G | |
878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 1136 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2)(3,10,12,7)(4,8,14,15)(5,9)(6,11)(13,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(1,3)(2,6)(4,11)(5,12)(7,15)(8,10)(9,16)(13,14);(1,3)(2,7)(4,13)(5,12)(6,15)(8,16)(9,10)(11,14)2414 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 5755);