Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #64425 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C7 |
| direct product | C22×#64425 |
| Fitting, socle | C22×C72 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C23×C3 |
| Hall | C22×C7⋊D7 ⋊ C3 |
| Hall | #3862 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #64425 |
| commutator, cosocle, hypocenter | C72 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C22×ΓL(1,𝔽8)⋊AGL(1,𝔽7), D4×#64425, #72222022, … |
| maximal normal subgroup of | C22×ΓL(1,𝔽8)⋊AGL(1,𝔽7), D4×#64425, #72222022, … |
| maximal quotient of | D4×#64425, C22×#11924339, C2×D3×#64425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 246);