Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C2×#127×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2818 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C2×#127×C59 | C2 |
| hypercenter | C2×#127 | D59 |
| hypocenter | C59 | #2818 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
630 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 133 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,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,h^b=h^58,d^c=de838 conjugacy classes — view the full character table.
| maximal subgroup of | #28564159, #28564163, #28564181, … |
| maximal normal subgroup of | #28564159, #28564163, #28564181, … |
| maximal quotient of | #28519348, #28519359, #28519728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 12551);