Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×C22⋊Dic59 |
| Sylow | C59 ⋊ Q8×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C23×Q8×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C23×Q8 | D59 |
| hypocenter | C59 | Q8×C22⋊C4 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
820 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 333 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28485127, #28485131, #28485155, … |
| maximal normal subgroup of | #28485127, #28485131, #28485155, … |
| maximal quotient of | C4⋊C4×C22⋊Dic59, Q8×C59⋊#95, #28510227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7346);