Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#14273725 |
| Sylow | C59 ⋊ C4×C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator | C22×C59 | C23×C4 |
| Frattini | C23 | C23×D59 |
| Fitting | C2×C4×Q8×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×C4×Q8 | D59 |
| hypocenter | C59 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×Q8 | |
588 conjugacy classes of subgroups.
1216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28483336, #28483337, #28483339, … |
| maximal normal subgroup of | #28483336, #28483337, #28483339, … |
| maximal quotient of | C4×#16837297, C4×#16837309, C4×#16837307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7078);