Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C32×C43 ⋊ C2 |
| Sylow | C43 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C2×D43 |
| commutator, socle | C2×C43 | C22×C16 |
| Frattini | C16 | C22×D43 |
| Fitting | C2×C32×C43 | C2 |
| hypercenter | C2×C32 | D43 |
| hypocenter | C43 | #2258 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C32 ◁ C2×C32 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,d^2=e,e^2=f,f^2=g,c^b=cg,h^c=h^421424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24984409, #24984411, #25017159, … |
| maximal normal subgroup of | #24984409, #24984411, #25017159, … |
| maximal quotient of | #25016775, #25016776, #25016792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6803);