Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C43 ⋊ M128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C2×D43 |
| commutator, socle | C2×C43 | C2×C32 |
| Fitting | C2×C32×C43 | C2 |
| hypercenter | C2×C32 | D43 |
| hypocenter | C43 | M128 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C32 ◁ C2×C32 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^421424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24984403, #24984404, #24984407, … |
| maximal normal subgroup of | #24984403, #24984404, #24984407, … |
| maximal quotient of | #24984402, C22⋊(C43⋊C64), C4⋊(C43⋊C64), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2721);