Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×(C2×D43)⋊C4 |
| Fitting | C2×C4×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ D4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C2×C4×D4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×C4×D4 | D43 |
| hypocenter | C43 | D4×C22⋊C4 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
1252 conjugacy classes of subgroups.
890 conjugacy classes — view the full character table.
| maximal subgroup of | #25112302, #25112303, #25112310, … |
| maximal normal subgroup of | #25112302, #25112303, #25112310, … |
| maximal quotient of | C22⋊C4×(C2×D43)⋊C4, C4⋊C4×(C2×D43)⋊C4, D4×C43⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7327);