Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #104 |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,3)(2,5)(4,7)(6,8)(12,13,14);(1,2,4,6,5,3,8,7)(10,11)(13,14);(9,10,11)Polycyclic presentation:
2^5,3^2|a^2=c,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^2,d^b=de54 conjugacy classes — view the full character table.
| maximal subgroup of | #10591664, #10591665, D3×#837, … |
| maximal normal subgroup of | #10591664, #10591665, D3×#837, … |
| maximal quotient of | #10589398, D4⋊(C3⋊(C3⋊C8)), #10589401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 312);