Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C22×#13063264 |
| Fitting | C22×C16×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D43 |
| commutator | C2×C43 | C23×C8 |
| Frattini | C8 | C23×D43 |
| Fitting | C22×C16×C43 | C2 |
| socle | C23×C43 | C2×C8 |
| hypercenter | C22×C16 | D43 |
| hypocenter | C43 | C22×M32 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C8 ◁ C22×C16 | |
400 conjugacy classes of subgroups.
1424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #25011435, #25011438, #25011468, … |
| maximal normal subgroup of | #25011435, #25011438, #25011468, … |
| maximal quotient of | C22×#14582674, C2×C4×#13063264, C22×(C2×D43)⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17605);