Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11745400 |
| unambiguous semidirect product | D233⋊C42 |
| Fitting | C2×C4×C233 ⋊ C4 |
| derived, Sylow | C233 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11745400 |
| commutator, hypocenter | C233 | C2×C42 |
| Frattini | C2 | C22×#11745400 |
| Fitting | C2×C4×C233 | C4 |
| socle | C22×C233 | C2×C4 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C2×C4 | |
108 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | #28417300, #28417305, #28417307, … |
| maximal normal subgroup of | #28417300, #28417305, #28417307, … |
| maximal quotient of | C42×#11745400, C2×(C2×#11745400)⋊C4, #28417371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 222);