Finite Group DatabasebetaFinite Group Databasebeta| order | 6752 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C211⋊C32 |
| derived, Sylow | C211 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D211 |
| commutator, hypocenter | C211 | C32 |
| Fitting | C16×C211 | C2 |
| socle | C2×C211 | C16 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C16 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,211|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^2101712 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D211, C2×C211⋊C32, #27212979, … |
| maximal normal subgroup of | C32×D211, C2×C211⋊C32, #27212979, … |
| maximal quotient of | C211⋊C64, C2×C211⋊C32 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6752, 52);