Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D4×#11745664 |
| Sylow | C59 ⋊ D4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Fitting | C2×C4×D4×C59 | C2 |
| hypercenter | C2×C4×D4 | D59 |
| hypocenter | C59 | D4×M16 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×D4 | |
544 conjugacy classes of subgroups.
1210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28483015, #28483019, #28483029, … |
| maximal normal subgroup of | #28483015, #28483019, #28483029, … |
| maximal quotient of | D8×#11745664, #28560120, SD16×#11745664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13247);