Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#11745685 |
| Fitting | C2×C4×Q8×C59 ⋊ C2 |
| Sylow | C59 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C2×C4×Q8×C59 | C2 |
| hypercenter | C2×C4×Q8 | D59 |
| hypocenter | C59 | Q8×#41 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×Q8 | |
1068 conjugacy classes of subgroups.
1210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28480730, #28480734, #28555563, … |
| maximal normal subgroup of | #28480730, #28480734, #28555563, … |
| maximal quotient of | C4⋊C4×#11745685, Q8×#14273684, Q8×#14273686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18091);