Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×C4⋊C8×D59 |
| Fitting | C2×C4⋊C8×C59 ⋊ C2 |
| Sylow | C59 ⋊ C22×C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator | C2×C59 | C23×C8 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C2×C4⋊C8×C59 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | C2×C4⋊C8 | D59 |
| hypocenter | C59 | C22×C4⋊C8 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4⋊C8 | |
640 conjugacy classes of subgroups.
1240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1277, #28478149, #28478163, … |
| maximal normal subgroup of | D59×#1277, #28478149, #28478163, … |
| maximal quotient of | C2×#334×D59, C2×#335×D59, D59×#1564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13059);