Finite Group DatabasebetaFinite Group Databasebeta| order | 294 |
| isoclinism | isoclinic class of #64424 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C72 ⋊ C2×C3 |
| Hall | #3861 ⋊ C2 |
| Hall | C7⋊D7 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 49 |
A minimal faithful permutation representation — 3 generators on 14 points:
(2,6,5,3,4,7)(9,13,12,10,11,14);(8,9,12,13,11,14,10);(1,2,5,6,4,7,3)Polycyclic presentation:
2,3,7^2|c^a=c^6,d^a=d^6,c^b=c^4,d^b=d^414 conjugacy classes — view the full character table.
| maximal subgroup of | #5997⋊C3, #64423⋊C2, C2×#64424, … |
| maximal normal subgroup of | #5997⋊C3, #64423⋊C2, C2×#64424, … |
| maximal quotient of | #10596874, C2×#64424, #11725077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(294, 13);