Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of GL(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
| direct product | C4×GL(3,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C4 | GL(3,𝔽2) |
| commutator, hypocenter | GL(3,𝔽2) | C4 |
| Frattini, cosocle | C2 | C2×GL(3,𝔽2) |
| socle, prime radical | C2×GL(3,𝔽2) | C2 |
| LCS | G ▷ GL(3,𝔽2) | |
| UCS | C1 ◁ C4 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 28 |
24 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1046);