Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | SL(2,𝔽7) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, socle, hypercenter | C2 | SO(3,𝔽7) |
| commutator, cosocle, hypocenter | SL(2,𝔽7) | C2 |
| LCS | G ▷ SL(2,𝔽7) | |
| UCS | C1 ◁ C2 | |
34 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 16 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,10,5,9,13,14,6,3,16,2,4,7,8,12)(11,15);(2,16)(4,11)(5,10)(6,12)(7,14)(8,13)(9,15)16 conjugacy classes — view the full character table.
| maximal subgroup of | #13062002, #13062004, C2×#10621462, … |
| maximal normal subgroup of | #13062002, #13062004, C2×#10621462, … |
| maximal quotient of | #13057024, C2×#10621462, C3×#10621462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1044);