Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#13063331 |
| Fitting | C23×C8×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D43 |
| commutator | C2×C43 | C24×C4 |
| Frattini | C4 | C24×D43 |
| Fitting | C23×C8×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C23×C8 | D43 |
| hypocenter | C43 | C22×#131 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C8 ◁ C23×C8 | |
1504 conjugacy classes of subgroups.
1424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #25002008, #25002012, #25002030, … |
| maximal normal subgroup of | #25002008, #25002012, #25002030, … |
| maximal quotient of | C22×#14582853, C22×#14582854, C2×C4×#13063331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 19214);