Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#16837877 |
| Sylow | C59 ⋊ C2×#518 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D59 |
| commutator | C2×C59 | C24×C4 |
| Frattini | C22 | C24×D59 |
| Fitting | C23×D4×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C23×D4 | D59 |
| hypocenter | C59 | C2×#518 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
1920 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1920 conjugacy classes of subgroups — too many to draw. Only its 1077 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1228 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28494006, #28494009, #28494031, … |
| maximal normal subgroup of | #28494006, #28494009, #28494031, … |
| maximal quotient of | C2×#21426449, C2×#21426453, C2×#21426457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17697);