Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Fitting | C59×#322 ⋊ C2 |
| Sylow | C59 ⋊ #1450 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D59 |
| commutator | C2×C59 | C2×C4×C8 |
| Fitting | C59×#322 | C2 |
| socle | C22×C59 | C2×C42 |
| hypercenter | #322 | D59 |
| hypocenter | C59 | #1450 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C42 ◁ #322 | |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=e,d^2=f,e^2=g,h^a=h^58,c^b=cf,h^c=h^581240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28497692, #28497696, #28497743, … |
| maximal normal subgroup of | #28497692, #28497696, #28497743, … |
| maximal quotient of | #28478047, #28478073, #28479117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2795);