Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #455×D59 |
| Fitting | C59×#455 ⋊ C2 |
| Sylow | C59 ⋊ C2×#455 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #120×D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#455 | C2 |
| socle | C2×C59 | C2×#120 |
| hypercenter | #455 | D59 |
| hypocenter | C59 | C2×#455 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #455 | |
760 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
496 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1403, #28508926, D59×#2197, … |
| maximal normal subgroup of | D59×#1403, #28508926, D59×#2197, … |
| maximal quotient of | D59×#1601, D59×#1602, D59×#1607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13837);