Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| isoclinism | isoclinic class of Dic118 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×C8×Dic118 |
| Sylow | C59 ⋊ C2×C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D59 |
| commutator | C2×C59 | C23×C8 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C2×C4×C8×C59 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | C2×C4×C8 | D59 |
| hypocenter | C59 | C2×C8×Q8 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C8 ◁ C2×C4×C8 | |
440 conjugacy classes of subgroups.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14273645, #28479263, C8×#14273652, … |
| maximal normal subgroup of | C8×#14273645, #28479263, C8×#14273652, … |
| maximal quotient of | C2×C8×C4⋊Dic59, C2×C8×Dic59⋊C4, C4×C8×Dic118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13431);