Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of SL(2,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| direct product | C3×SL(2,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C2×C3 | GL(3,𝔽2) |
| commutator, hypocenter | SL(2,𝔽7) | C3 |
| Frattini, cosocle | C2 | C3×GL(3,𝔽2) |
| LCS | G ▷ SL(2,𝔽7) | |
| UCS | C1 ◁ C2×C3 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
33 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 517);