Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C82×C59 ⋊ C2 |
| Sylow | C59 ⋊ #1454 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D59 |
| commutator, socle | C22×C59 | C2×C42 |
| Fitting | C82×C59 | C2 |
| hypercenter | C82 | D59 |
| hypocenter | C59 | #1454 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C42 ◁ C82 | |
178 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cfg,c^b=cf,h^c=h^581912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1454, C2×#21422395, #28554321, … |
| maximal normal subgroup of | D59×#1454, C2×#21422395, #28554321, … |
| maximal quotient of | #28478061, #28478079, #28479123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2809);