Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C4×C8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2922 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C2×C4×C8×C59 | C2 |
| hypercenter | C2×C4×C8 | D59 |
| hypocenter | C59 | #2922 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C42 ◁ C2×C4×C8 | |
400 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 400 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|a^2=f,c^2=e,f^2=g,b^a=be,d^b=dg,h^b=h^581912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479379, #28479381, #28479384, … |
| maximal normal subgroup of | #28479379, #28479381, #28479384, … |
| maximal quotient of | #28586173, C4×#16837368, C4×#16837428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13152);