Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C173 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #10621924 |
| commutator, hypocenter | C173 | C32 |
| Fitting | C8×C173 | C4 |
| socle | C2×C173 | C16 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,173|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^80,f^b=f^172376 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#19149729, D173⋊C32, #26012423, … |
| maximal normal subgroup of | C2×#19149729, D173⋊C32, #26012423, … |
| maximal quotient of | #26012330, C2×#19149729 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 196);