Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| isoclinism | isoclinic class of D233 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4×D233 |
| Fitting | C22×C4×C233 ⋊ C2 |
| derived, Sylow | C233 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D233 |
| commutator, hypocenter | C233 | C23×C4 |
| Frattini | C2 | C23×D233 |
| Fitting | C22×C4×C233 | C2 |
| socle | C23×C233 | C22 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C22×C4 | |
236 conjugacy classes of subgroups.
1888 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #95×D233, #28416282, C4×#16836571, … |
| maximal normal subgroup of | #95×D233, #28416282, C4×#16836571, … |
| maximal quotient of | C2×C42×D233, C22×C4×Dic233, C2×C22⋊C4×D233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 180);