Finite Group DatabasebetaFinite Group Databasebeta| order | 30300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | D3×#14579003⋊C2 |
| unambiguous semidirect product | (C3×#14579003⋊C2)⋊C2 |
| unambiguous semidirect product | (D3×#14579003)⋊C2 |
| unambiguous semidirect product | (C3⋊(#14579003⋊C2))⋊C2 |
| derived, Hall | C3×C101 ⋊ C22×C25 |
| Hall | C3×#14579003 ⋊ C22 |
| Hall | #14579003 ⋊ C2×D3 |
| Hall | D3×D101 ⋊ C25 |
| Sylow | C101 ⋊ C2×D3×C25 |
| Sylow | C3 ⋊ C2×#14579003⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D3×D101⋊C5 |
| commutator, hypocenter | C3×C101 | C22×C25 |
| Fitting, socle, cosocle | C3×C5×C101 | C22×C5 |
| prime radical | C5×D3×D101 | C5 |
| LCS | G ▷ C3×C101 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7575 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30300, 16);