Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#14273661 |
| Sylow | C59 ⋊ C22×#107 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D236 |
| commutator | C4×C59 | C23×C4 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C23×C8×C59 | C2 |
| socle | C24×C59 | D4 |
| hypercenter | C23×C8 | D59 |
| hypocenter | C59 | C22×#107 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
600 conjugacy classes of subgroups.
1912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28494587, #28494589, #28494591, … |
| maximal normal subgroup of | #28494587, #28494589, #28494591, … |
| maximal quotient of | C22×#16837155, C2×#21422855, C2×#21422871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13085);