Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C59×M64 ⋊ C2 |
| Sylow | C59 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D59 |
| commutator, socle | C2×C59 | C22×C16 |
| Fitting | C59×M64 | C2 |
| hypercenter | M64 | D59 |
| hypocenter | C59 | #2258 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C16 ◁ M64 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^58,c^b=cg,h^c=h^581240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28509250, #28509252, #28509255, … |
| maximal normal subgroup of | #28509250, #28509252, #28509255, … |
| maximal quotient of | #28508870, #28508871, #28508884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6805);