Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C82×D59 |
| Fitting | C82×C59 ⋊ C2 |
| derived, Sylow | C59 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C82 | D59 |
| commutator, hypocenter | C59 | C2×C82 |
| Frattini | C42 | C22×D59 |
| Fitting | C82×C59 | C2 |
| socle | C22×C59 | C2×C42 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C82 | |
280 conjugacy classes of subgroups.
1984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×C16×D59, D59×#1311, C8×#14273666, … |
| maximal normal subgroup of | C8×C16×D59, D59×#1311, C8×#14273666, … |
| maximal quotient of | C82×Dic59, D59×#1273, #28479111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2782);