Finite Group DatabasebetaFinite Group Databasebeta| order | 10772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C2693 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2693 | C4 |
| prime radical, cosocle | D2693 | C2 |
| LCS | G ▷ C2693 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,2693|a^2=b,c^a=c^1834,c^b=c^2692677 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#24924673, C3×#24924673, C3⋊#24924673 |
| maximal normal subgroup of | C2×#24924673, C3×#24924673 |
| maximal quotient of | #36340644, C2×#24924673, C3×#24924673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10772, 3);