Finite Group DatabasebetaFinite Group Databasebeta| order | 945 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C5 · Schur multiplier (H2) = C33 |
| Fitting, socle | C32×C5×C7 ⋊ C3 |
| derived, Sylow | C7 ⋊ C33×C5 |
| Hall | C5×C7 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7 | C33×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C32×C5 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 315 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(945, 12);