Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| isoclinism | isoclinic class of D233 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C8×D233 |
| Fitting | C2×C8×C233 ⋊ C2 |
| derived, Sylow | C233 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D233 |
| commutator, hypocenter | C233 | C22×C8 |
| Frattini | C4 | C22×D233 |
| Fitting | C2×C8×C233 | C2 |
| socle | C22×C233 | C2×C4 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C2×C8 | |
76 conjugacy classes of subgroups.
1888 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28416214, C4×C8×D233, #97×D233, … |
| maximal normal subgroup of | #28416214, C4×C8×D233, #97×D233, … |
| maximal quotient of | C4×C8×D233, C2×C8×Dic233, C22⋊C8×D233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 147);