Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×C43⋊C8 |
| Sylow | C43 ⋊ C8×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D43 |
| commutator | C2×C43 | C2×C4×C8 |
| Fitting | C4×M16×C43 | C2 |
| socle | C22×C43 | C2×C42 |
| hypercenter | C4×M16 | D43 |
| hypocenter | C43 | C8×M16 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C42 ◁ C4×M16 | |
224 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
920 conjugacy classes — view the full character table.
| maximal subgroup of | #24987154, #100×C43⋊C8, #24987159, … |
| maximal normal subgroup of | #24987154, #100×C43⋊C8, #24987159, … |
| maximal quotient of | #97×C43⋊C8, #24985978, #24987022, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2788);