Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#14273655 |
| Fitting | C43×C59 ⋊ C2 |
| Sylow | C59 ⋊ C4×#104 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | D236 |
| commutator | C4×C59 | C2×C42 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C43×C59 | C2 |
| socle | C22×C59 | C2×C22⋊C4 |
| hypercenter | C43 | D59 |
| hypocenter | C59 | C4×#104 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C42 ◁ C2×C42 ◁ C43 | |
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479394, C8×#14273655, #28479401, … |
| maximal normal subgroup of | #28479394, C8×#14273655, #28479401, … |
| maximal quotient of | C4×#16837131, C4×#16837134, #28479302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4316);