Finite Group DatabasebetaFinite Group Databasebeta| order | 30450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52×C29 · Schur multiplier (H2) = C5 |
| direct product | C3×C52×D7×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52×C29 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C3×C52×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7×C29 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C52×C29 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15225 |
10875 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30450, 85);