Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#11745400 |
| unambiguous semidirect product | D233⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×#11745400)⋊C22 |
| Fitting | C23×C233 ⋊ C4 |
| Sylow | C233 ⋊ C2×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#11745400 |
| commutator | C2×C233 | C22×C4 |
| Frattini | C2 | C22×#11745400 |
| Fitting | C23×C233 | C4 |
| socle | C22×C233 | C2×C4 |
| hypercenter | C23 | #11745400 |
| hypocenter | C233 | C2×C22⋊C4 |
| LCS | G ▷ C2×C233 ▷ C233 | |
| UCS | C1 ◁ C22 ◁ C23 | |
132 conjugacy classes of subgroups.
484 conjugacy classes — view the full character table.
| maximal subgroup of | #28417312, #28417313, C4×C22⋊#11745400, … |
| maximal normal subgroup of | #28417312, #28417313, C4×C22⋊#11745400, … |
| maximal quotient of | C2×(C2×#11745400)⋊C4, C4×C22⋊#11745400, #28417376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 223);