Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1378 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22⋊Dic43 |
| commutator | C22×C43 | C4×C8 |
| Frattini | C22×C8 | C2×D43 |
| Fitting | C2×M32×C43 | C2 |
| socle | C2×C43 | #336 |
| hypercenter | C2×M32 | D43 |
| hypocenter | C43 | #1378 |
| LCS | G ▷ C22×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C8 ◁ C22×C8 ◁ C2×M32 | |
132 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,e^a=eg,c^b=cg,h^b=h^42884 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1378, C2×#19132680, #25011618, … |
| maximal normal subgroup of | D43×#1378, C2×#19132680, #25011618, … |
| maximal quotient of | #24983432, #24983442, #24983449, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2595);