Finite Group DatabasebetaFinite Group Databasebeta| order | 1308 |
| isoclinism | isoclinic class of D109⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic109⋊C3 |
| derived, Sylow | C109 ⋊ C3×C4 |
| Hall | Dic109 ⋊ C3 |
| Hall | C109⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D109⋊C3 |
| commutator, hypocenter | C109 | C3×C4 |
| Fitting, socle, cosocle | C2×C109 | C2×C3 |
| prime radical | C2×C109⋊C3 | C2 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 436 |
Polycyclic presentation:
2,3,2,109|a^2=c,d^a=d^108,d^b=d^4548 conjugacy classes — view the full character table.
| maximal subgroup of | #16840993, C3×Dic109⋊C3, C3⋊(Dic109⋊C3), … |
| maximal normal subgroup of | #16840993, C3×Dic109⋊C3, C11×Dic109⋊C3, … |
| maximal quotient of | #16840975, C3×Dic109⋊C3, C3⋊(Dic109⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1308, 1);