Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of A4×C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C7 |
| direct product | A4×C7⋊D7 |
| Fitting, socle, derived | C22×C72 ⋊ C2×C3 |
| Hall | C22×C7⋊D7 ⋊ C3 |
| Sylow | C72 ⋊ C2×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C72 | C2×C3 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 196 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊A4×C7⋊D7, A4×#64424, S4×C7⋊D7, … |
| maximal normal subgroup of | A4×#64424, S4×C7⋊D7, A4×D72, … |
| maximal quotient of | C22⋊A4×C7⋊D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 259);