Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #3862 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C7 |
| direct product | C8×#3862 |
| Fitting, Hall | C72×C8 ⋊ C3 |
| derived, Sylow | C72 ⋊ C3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #3862 |
| commutator, hypocenter | C72 | C3×C8 |
| Frattini | C4 | C2×#3862 |
| Fitting | C72×C8 | C3 |
| socle | C2×C72 | C3×C4 |
| prime radical | C2×#3862 | C4 |
| cosocle | C4×C72 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#64425, M16×#3862, #72245215, … |
| maximal normal subgroup of | C8×#64425, M16×#3862, #72245215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 67);