Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2293 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator | C22×C59 | C23×C4 |
| Frattini | C23 | C23×D59 |
| Fitting | C4×C4⋊C4×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C4×C4⋊C4 | D59 |
| hypocenter | C59 | #2293 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
652 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 217 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,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,h^b=h^581216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479325, #28479335, #28479345, … |
| maximal normal subgroup of | #28479325, #28479335, #28479345, … |
| maximal quotient of | #28509798, #28509830, C4×#16837291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6971);