Finite Group DatabasebetaFinite Group Databasebeta| order | 27300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×ΓL(1,𝔽8)×D25 |
| unambiguous semidirect product | C25⋊(C22×C13×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C2×C25)⋊(C2×C13×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C2×C7×D25)⋊(C3×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | ΓL(1,𝔽8)×D25 |
| commutator, cosocle, hypocenter | C7×C25 | C22×C3×C13 |
| Frattini | C5 | C2×D5×C13×ΓL(1,𝔽8) |
| Fitting | C2×C7×C13×C25 | C2×C3 |
| socle | C2×C5×C7×C13 | C3×D5 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C2×C13 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4550 |
1820 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27300, 146);