Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of C22⋊#3862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C22⋊#3862 |
| Fitting, socle, Hall | C23×C72 ⋊ C3 |
| derived | C22×C72 ⋊ C2×C3 |
| Sylow | C72 ⋊ C2×A4 |
| Sylow | C23 ⋊ #3862 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C22⋊#3862 |
| commutator, cosocle, hypocenter | C22×C72 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C72 | C3 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 42 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C22⋊#3862, C2×#3861⋊A4, C2×#11924339 |
| maximal normal subgroup of | C22×C22⋊#3862, C2×#3861⋊A4, C2×#11924339 |
| maximal quotient of | C22×C22⋊#3862 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 273);