Finite Group DatabasebetaFinite Group Databasebeta| order | 147 |
| isoclinism | isoclinic class of #3861 |
| automorphism | Aut(G) order 98784 |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C72 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 49 |
A minimal faithful permutation representation — 3 generators on 14 points:
(2,3,4)(5,7,6)(9,10,11)(12,14,13);(8,9,10,12,11,13,14);(1,2,3,5,4,6,7)Polycyclic presentation:
3,7^2|b^a=b^2,c^a=c^219 conjugacy classes — view the full character table.
| maximal subgroup of | #64423, #64424, C2×#3861, … |
| maximal normal subgroup of | #64423, #64424, C2×#3861, … |
| maximal quotient of | C2×#3861, #89204, C3×#3861, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(147, 4);