Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×C43⋊C16 |
| derived, Sylow | C43 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D43 |
| commutator, hypocenter | C43 | C23×C16 |
| Frattini | C8 | C23×D43 |
| Fitting | C23×C8×C43 | C2 |
| socle | C24×C43 | C8 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C23×C8 | |
440 conjugacy classes of subgroups.
1472 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#19132672, C2×#19132673, #25011440, … |
| maximal normal subgroup of | C2×#19132672, C2×#19132673, #25011440, … |
| maximal quotient of | C22×C4×C43⋊C16, C22×C22⋊(C43⋊C16), C22×C4⋊(C43⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17603);