Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#14582863 |
| Sylow | C43 ⋊ C2×#407 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator | C22×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C24×C4×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C24×C4 | D43 |
| hypocenter | C43 | C2×#407 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 | |
1008 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24986196, #24986197, #24986202, … |
| maximal normal subgroup of | #24986196, #24986197, #24986202, … |
| maximal quotient of | C2×#19132922, C2×#19132925, C2×#19132929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12946);