Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1276 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | D236 |
| commutator | C4×C59 | C4×C8 |
| Frattini | C2×C42 | C2×D59 |
| Fitting | C43×C59 | C2 |
| socle | C22×C59 | #95 |
| hypercenter | C43 | D59 |
| hypocenter | C59 | #1276 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C42 ◁ C2×C42 ◁ C43 | |
208 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=e,c^2=f,d^2=g,b^a=bc,c^a=cf,e^a=ef,h^a=h^581912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475440, #28475441, #28475512, … |
| maximal normal subgroup of | #28475440, #28475441, #28475512, … |
| maximal quotient of | #28475217, #28475221, #28475225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2343);