Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of (C2×AGL(1,𝔽5))⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×(C2×AGL(1,𝔽5))⋊D5 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊(C3×D5) |
| Hall | C3×C52 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ C3×C22⋊C4 |
146 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3)(5,7)(9,10)(11,12)(13,14,15,17,16);(4,5)(6,7)(8,9,11,12,10)(14,15,16,17)102 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×C22⋊AGL(1,𝔽5), D3×(C2×AGL(1,𝔽5))⋊D5, #72230095 |
| maximal normal subgroup of | C3×D5×C22⋊AGL(1,𝔽5), D3×(C2×AGL(1,𝔽5))⋊D5, #72230095 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 532);