Finite Group DatabasebetaFinite Group Databasebeta| order | 27090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×C5×#14268593 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #14268593 |
| commutator, cosocle, hypocenter | C7×C43 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C43 | C2×C3 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C3×C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4515 |
840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27090, 93);