Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | #431×D43 |
| Fitting | C43×#431 ⋊ C2 |
| Sylow | C43 ⋊ C2×#431 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D43 |
| commutator | C2×C43 | C23×C8 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#431 | C2 |
| socle | C22×C43 | C23×C4 |
| hypercenter | #431 | D43 |
| hypocenter | C43 | C2×#431 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C42 ◁ #431 | |
528 conjugacy classes of subgroups.
920 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1274, #24985994, #24986003, … |
| maximal normal subgroup of | D43×#1274, #24985994, #24986003, … |
| maximal quotient of | D43×#1744, C4×C22⋊C8×D43, C4×C4⋊C8×D43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13122);