Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#388 ⋊ C2 |
| Sylow | C59 ⋊ #2534 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C59×#388 | C2 |
| hypercenter | #388 | D59 |
| hypocenter | C59 | #2534 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #388 | |
800 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=eg,b^a=be,c^a=cf,d^a=de,h^a=h^58,c^b=cg,h^b=h^58,h^d=h^58850 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2534, C2×#21428990, #28758871, … |
| maximal normal subgroup of | D59×#2534, C2×#21428990, #28758871, … |
| maximal quotient of | #28510912, #28511408, #28511463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 9404);