Finite Group DatabasebetaFinite Group Databasebeta| order | 6724 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C41 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C412 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C412 | C4 |
| LCS | G ▷ C412 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,41^2|a^2=b,c^a=c^32,d^a=d^9,c^b=c^40,d^b=d^40424 conjugacy classes — view the full character table.
| maximal subgroup of | #34118107, C3×#20269609, C3⋊#20269609, … |
| maximal normal subgroup of | C3×#20269609, #46777413, #46777418, … |
| maximal quotient of | C3×#20269609, C3⋊#20269609, C5×#20269609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6724, 14);