Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C37 · Schur multiplier (H2) = C2 |
| direct product | #104×C37 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C37 | D4 |
| commutator | C4 | C2×C4×C37 |
| Frattini, cosocle | C2×C4 | C22×C37 |
| socle | C2×C37 | C22⋊C4 |
| prime radical | #41×C37 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C37 ◁ C2×C4×C37 ◁ G | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 296 |
A minimal faithful permutation representation — 2 generators on 45 points:
(1,2,4,7,5,3,8,6)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(1,3)(2,5)(4,6)(7,8)518 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 11);