Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | #340×D59 |
| Fitting | C59×#340 ⋊ C2 |
| Sylow | C59 ⋊ C2×#340 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D59 |
| commutator | C4×C59 | C2×C42 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#340 | C2 |
| socle | C23×C59 | C2×D4 |
| hypercenter | #340 | D59 |
| hypocenter | C59 | C2×#340 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
512 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 193 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
868 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1347, D59×#1348, #28498919, … |
| maximal normal subgroup of | D59×#1347, D59×#1348, #28498919, … |
| maximal quotient of | D59×#1277, #28478153, #28478163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4222);