Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C43×M64 ⋊ C2 |
| Sylow | C43 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D43 |
| commutator, socle | C2×C43 | C22×C16 |
| Fitting | C43×M64 | C2 |
| hypercenter | M64 | D43 |
| hypocenter | C43 | #2258 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C16 ◁ M64 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^42,c^b=cg,h^c=h^42920 conjugacy classes — view the full character table.
| maximal subgroup of | #25017158, #25017160, #25017163, … |
| maximal normal subgroup of | #25017158, #25017160, #25017163, … |
| maximal quotient of | #25016778, #25016779, #25016792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6805);