Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#431 ⋊ C2 |
| Sylow | C59 ⋊ C8×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D59 |
| commutator | C2×C59 | C23×C8 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#431 | C2 |
| socle | C22×C59 | C23×C4 |
| hypercenter | #431 | D59 |
| hypocenter | C59 | C8×#41 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C42 ◁ #431 | |
456 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,h^c=h^581240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479394, #28479396, #28479401, … |
| maximal normal subgroup of | #28479394, #28479396, #28479401, … |
| maximal quotient of | #28586890, #28586895, C4×(C22⋊D59)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13466);