Finite Group DatabasebetaFinite Group Databasebeta| order | 30084 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(Dic109⋊C3) |
| unambiguous semidirect product | Dic2507⋊C3 |
| derived, Hall | C23×C109 ⋊ C3×C4 |
| Hall | Dic2507 ⋊ C3 |
| Hall | C23×C109⋊C3 ⋊ C4 |
| Hall | C109⋊C3 ⋊ Dic23 |
| Sylow | C109 ⋊ C3×Dic23 |
| Sylow | C23 ⋊ Dic109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C23⋊(D109⋊C3) |
| commutator, hypocenter | C23×C109 | C3×C4 |
| Fitting, socle, cosocle | C2×C23×C109 | C2×C3 |
| prime radical | C2×C23×C109⋊C3 | C2 |
| LCS | G ▷ C23×C109 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10028 |
Polycyclic presentation:
2,3,23,109,2|a^2=e,c^a=c^22,d^a=d^108,d^b=d^63906 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30084, 12);