Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×Q8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2637 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C2×C4×Q8×C59 | C2 |
| hypercenter | C2×C4×Q8 | D59 |
| hypocenter | C59 | #2637 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
450 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 141 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=e,b^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^581192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28562124, #28562128, #28562154, … |
| maximal normal subgroup of | #28562124, #28562128, #28562154, … |
| maximal quotient of | #28515158, #28515188, #28515361, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 10416);