Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | #6511 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #131 |
| Sylow | C7 ⋊ C3×#131 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^3,3,2^2,7|a^2=e,e^2=f,g^a=g^6,c^b=cf,g^d=g^470 conjugacy classes — view the full character table.
| maximal subgroup of | #89595⋊C3, #89596⋊C3, #89968⋊C3, … |
| maximal normal subgroup of | #89595⋊C3, #89596⋊C3, #89968⋊C3, … |
| maximal quotient of | #89769⋊C3, #89771⋊C3, #89772⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 366);