Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| isoclinism | isoclinic class of A4⋊D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | C2×A4⋊D13 |
| unambiguous semidirect product | (C2×A4)⋊D13 |
| unambiguous semidirect product | (C2×C13)⋊S4 |
| Fitting, socle | C23×C13 ⋊ D3 |
| derived | A4×C13 ⋊ C22 |
| Sylow | C13 ⋊ C2×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4⋊D13 |
| commutator, cosocle, hypocenter | A4×C13 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C23×C13 | D3 |
| LCS | G ▷ A4×C13 | |
| UCS | C1 ◁ C2 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 78 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | #11929072, #11929073, #11929076, … |
| maximal normal subgroup of | #11929072, #11929073, #11929076, … |
| maximal quotient of | #11929119, C4×A4⋊D13, C4⋊(A4⋊D13), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 245);