Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of GL(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| direct product | C9×GL(3,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C9 | GL(3,𝔽2) |
| commutator, hypocenter | GL(3,𝔽2) | C9 |
| Frattini, cosocle | C3 | C3×GL(3,𝔽2) |
| socle, prime radical | C3×GL(3,𝔽2) | C3 |
| LCS | G ▷ GL(3,𝔽2) | |
| UCS | C1 ◁ C9 | |
55 conjugacy classes of subgroups.
| transitive degree | μt(G) = 63 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C9×GL(3,𝔽2) |
| maximal normal subgroup of | C2×C9×GL(3,𝔽2) |
| maximal quotient of | C2×C9×GL(3,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 437);