Finite Group DatabasebetaFinite Group Databasebeta| order | 6824 |
| automorphism | Aut(G) order 5814048 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3412 |
| unambiguous semidirect product | C4⋊D853 |
| Fitting | C4×C853 ⋊ C2 |
| Sylow | C853 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D853 |
| commutator, socle | C2×C853 | C22 |
| Fitting | C4×C853 | C2 |
| hypercenter | C4 | D853 |
| hypocenter | C853 | D4 |
| LCS | G ▷ C2×C853 ▷ C853 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,853|b^a=bc,d^a=d^852,d^b=d^8521709 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28331485, D6824, #28331487, … |
| maximal normal subgroup of | #28331485, D6824, #28331487, … |
| maximal quotient of | #28331477, C4⋊Dic853, D6824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6824, 10);