Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×C5×D169 |
| Fitting | C2×C32×C5×C169 ⋊ C2 |
| derived, Sylow | C169 ⋊ C22×C32×C5 |
| Hall | C32×C5×C169 ⋊ C22 |
| Hall | C32×C169 ⋊ C22×C5 |
| Hall | C5×C169 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C5 | D169 |
| commutator, cosocle, hypocenter | C169 | C22×C32×C5 |
| Frattini | C13 | C2×C32×C5×D13 |
| Fitting | C2×C32×C5×C169 | C2 |
| socle | C2×C32×C5×C13 | D13 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C2×C32×C5 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15210 |
7740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 165);