Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C4×#10621872 |
| Fitting | C2×C4×C8×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×D43 |
| commutator | C2×C43 | C22×C42 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C2×C4×C8×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C2×C4×C8 | D43 |
| hypocenter | C43 | C2×C4×M16 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C42 ◁ C2×C4×C8 | |
656 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 357 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24985977, #24985984, #24985989, … |
| maximal normal subgroup of | #24985977, #24985984, #24985989, … |
| maximal quotient of | C2×C8×#10621872, C2×#19132881, C2×#19132889, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12916);