Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #2163 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D43 |
| commutator, socle | C22×C43 | C22×C8 |
| Fitting | C2×C4×C8×C43 | C2 |
| hypercenter | C2×C4×C8 | D43 |
| hypocenter | C43 | #2163 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C4×C8 | |
152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 93 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=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^421400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24983440, #24983441, #24983442, … |
| maximal normal subgroup of | #24983440, #24983441, #24983442, … |
| maximal quotient of | #25011599, #25011628, #25011906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6313);