Finite Group DatabasebetaFinite Group Databasebeta| order | 6824 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C853 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #16811794 |
| commutator, hypocenter | C853 | C8 |
| Fitting, socle | C2×C853 | C4 |
| LCS | G ▷ C853 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,853|a^2=b,b^2=c,d^a=d^333,d^b=d^852434 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20291967, D853⋊C8, #28331509, … |
| maximal normal subgroup of | C2×#20291967, D853⋊C8, #28331509, … |
| maximal quotient of | #28331503, C2×#20291967 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6824, 13);