Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#14273734 |
| Sylow | C59 ⋊ C22×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator | C2×C59 | C24×C4 |
| Frattini | C4 | C24×D59 |
| Fitting | C22×#41×C59 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | C22×#41 | D59 |
| hypocenter | C59 | C22×#131 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
1504 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 1077 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28494101, #28494105, #28494121, … |
| maximal normal subgroup of | #28494101, #28494105, #28494121, … |
| maximal quotient of | C22×#16837358, C2×C4×#14273734, C22×#16837369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 19215);