Finite Group DatabasebetaFinite Group Databasebeta| order | 294 |
| isoclinism | isoclinic class of #64418 |
| automorphism | Aut(G) = (#64418⋊C2)⋊C3 (order 1764) · Inn(G) = G · Out(G) = C2×C3 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C72 ⋊ D3 |
| derived, Hall | #3862 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #3862 | C2 |
| Fitting, socle | C72 | D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 | |
14 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 14 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,6,12,7,9,2,3,10,13,11,8,4,5,14);(3,5,8)(4,6,7)(9,13,12)(10,14,11)Polycyclic presentation:
2,3,7^2|b^a=b^2,c^a=d,d^a=c,c^b=c^2,d^b=d^420 conjugacy classes — view the full character table.
| maximal subgroup of | #64418⋊C2, C2×#64418, #64418⋊C3, … |
| maximal normal subgroup of | #64418⋊C2, C2×#64418, #64418⋊C3, … |
| maximal quotient of | #10596868, C2×#64418, #11725071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(294, 7);