Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×Dic59 |
| Sylow | C59 ⋊ C4×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator | C2×C59 | C24×C4 |
| Fitting | C2×H(5,𝔽2)×C59 | C2 |
| socle | C22×C59 | C25 |
| hypercenter | C2×H(5,𝔽2) | D59 |
| hypocenter | C59 | C4×H(5,𝔽2) |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
1660 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 1063 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28594558, #453×Dic59, #28594569, … |
| maximal normal subgroup of | #28594558, #453×Dic59, #28594569, … |
| maximal quotient of | #518×Dic59, #520×Dic59, #534×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17718);