Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C22⋊C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C22×C22⋊C4×C59 | C2 |
| hypercenter | C22×C22⋊C4 | D59 |
| hypocenter | C59 | #2405 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^58,c^b=cg1198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28486591, #28486593, #28486601, … |
| maximal normal subgroup of | #28486591, #28486593, #28486601, … |
| maximal quotient of | #28510555, #28510573, #28511470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7837);