Finite Group DatabasebetaFinite Group Databasebeta| order | 8868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C739⋊C3)⋊C4 |
| unambiguous semidirect product | Dic739⋊C3 |
| derived, Sylow | C739 ⋊ C3×C4 |
| Hall | Dic739 ⋊ C3 |
| Hall | C739⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D739⋊C3 |
| commutator, hypocenter | C739 | C3×C4 |
| Fitting, socle | C2×C739 | C2×C3 |
| LCS | G ▷ C739 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,739,2|a^2=d,c^a=c^738,c^b=c^320258 conjugacy classes — view the full character table.
| maximal subgroup of | #20268987⋊C4, C3×(C739⋊C3)⋊C4, C3⋊((C739⋊C3)⋊C4) |
| maximal normal subgroup of | #20268987⋊C4, C3×(C739⋊C3)⋊C4 |
| maximal quotient of | #20268985⋊C4, C3×(C739⋊C3)⋊C4, C3⋊((C739⋊C3)⋊C4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8868, 2);