Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D932 |
| Fitting | C42×C233 ⋊ C2 |
| Sylow | C233 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D233 |
| commutator | C2×C233 | C22×C4 |
| Frattini | C22 | C22×D233 |
| Fitting | C42×C233 | C2 |
| socle | C22×C233 | C23 |
| hypercenter | C42 | D233 |
| hypocenter | C233 | C4×D4 |
| LCS | G ▷ C2×C233 ▷ C233 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
94 conjugacy classes of subgroups.
1876 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28416162, #28416164, #28416500, … |
| maximal normal subgroup of | #28416162, #28416164, #28416500, … |
| maximal quotient of | C4×#16836571, C4×C4⋊Dic233, #28416309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 110);