Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C37 · Schur multiplier (H2) = C2 |
| direct product | #100×C37 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | C22⋊C4 |
| commutator | C22 | C2×C4×C37 |
| Frattini, cosocle | C2×C4 | C22×C37 |
| prime radical | C2×D4×C37 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ G | |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 296 |
A minimal faithful permutation representation — 2 generators on 45 points:
(1,2,3,6,4,5,7,8)(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);(2,5)(3,7)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 7);