Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #64418 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×#64418 |
| Fitting, socle | C22×C72 ⋊ D3 |
| derived, Hall | #3862 ⋊ C23 |
| Sylow | C72 ⋊ C22×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #64418 |
| commutator, cosocle, hypocenter | #3862 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72 | D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C22 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 239);