Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #398×D43 |
| Fitting | C43×#398 ⋊ C2 |
| Sylow | C43 ⋊ C2×#398 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#398 | C2 |
| hypercenter | #398 | D43 |
| hypocenter | C43 | C2×#398 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #398 | |
692 conjugacy classes of subgroups.
506 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1346, #25007281, D43×#1609, … |
| maximal normal subgroup of | D43×#1346, #25007281, D43×#1609, … |
| maximal quotient of | D43×#1441, D43×#1442, D43×#1444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7739);