Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | C2×#14582732 |
| Fitting | C2×C32×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×M64 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16 | C2×D43 |
| commutator | C2×C43 | C22×C16 |
| Frattini | C16 | C22×D43 |
| Fitting | C2×C32×C43 | C2 |
| socle | C22×C43 | C2×C16 |
| hypercenter | C2×C32 | D43 |
| hypocenter | C43 | C2×M64 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C16 ◁ C2×C32 | |
112 conjugacy classes of subgroups.
1424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24984407, C4×#14582732, #25016773, … |
| maximal normal subgroup of | #24984407, C4×#14582732, #25016773, … |
| maximal quotient of | C2×#19132728, C4×#14582732, C2×(C2×D43)⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6801);