Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×#117×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2280 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator | C22×C59 | C23×C4 |
| Frattini | C23 | C23×D59 |
| Fitting | C2×#117×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×#117 | D59 |
| hypocenter | C59 | #2280 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#117 | |
1088 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=g,d^2=e,b^a=be,c^a=cf,h^c=h^581216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28493919, #28493923, #28493929, … |
| maximal normal subgroup of | #28493919, #28493923, #28493929, … |
| maximal quotient of | #28509786, #28509804, C4×#16837257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6889);