Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | #394×D43 |
| Fitting | C43×#394 ⋊ C2 |
| Sylow | C43 ⋊ C2×#394 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#394 | C2 |
| hypercenter | #394 | D43 |
| hypocenter | C43 | C2×#394 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #394 | |
1252 conjugacy classes of subgroups.
506 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1345, #25007277, D43×#1597, … |
| maximal normal subgroup of | D43×#1345, #25007277, D43×#1597, … |
| maximal quotient of | D43×#1438, D43×#1439, D43×#1440, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7712);