Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of SL(2,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| direct product | C2×SL(2,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C22 | GL(3,𝔽2) |
| commutator, hypocenter | SL(2,𝔽7) | C2 |
| Frattini, cosocle | C2 | C2×GL(3,𝔽2) |
| LCS | G ▷ SL(2,𝔽7) | |
| UCS | C1 ◁ C22 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
22 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1048);