Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×#11745672 |
| Sylow | C59 ⋊ Q8×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C22⋊D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | Q82×C59 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | Q82 | D59 |
| hypocenter | C59 | Q8×Q16 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 ◁ Q82 | |
336 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
760 conjugacy classes — view the full character table.
| maximal subgroup of | #28578839, #28578842, #28578847, … |
| maximal normal subgroup of | #28578839, #28578842, #28578847, … |
| maximal quotient of | Q8×#14273650, Q8×#14273651, C4⋊C4×#11745672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17392);