Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C8 · Schur multiplier (H2) = C23 |
| direct product | C5×#4550 |
| Hall | C3×C5 ⋊ #336 |
| Sylow | C3 ⋊ C5×#336 |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(6,7,8)(14,16)(17,18,19,21,20,22,23,24);(7,8)(9,10,11,12)(13,14)(15,16)360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×#336, C2×C5×#4550, D5×#4550, … |
| maximal normal subgroup of | C5×D3×#336, C2×C5×#4550, D5×#4550, … |
| maximal quotient of | C5×C3⋊#1273, C5×#67737, C5×#67740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 444);