Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#11925359 |
| derived, Hall | C3×C52 ⋊ C2×C42 |
| Sylow | C52 ⋊ C2×C4×Dic3 |
| Sylow | C3 ⋊ C2×#87830 |
540 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(4,5,7,6)(9,10,13,12);(1,2,3)(14,15);(5,6,7,8)(10,11,13,12)(16,17,18,19)96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#87830, C2×#72229331, C2×#72224584, … |
| maximal normal subgroup of | C2×D3×#87830, C2×#72224584, C2×#72224581, … |
| maximal quotient of | #72230533, C2×#72229331, C2×#72224596 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,3)(4,5,7,6)(9,10,13,12), (1,2,3)(14,15), (5,6,7,8)(10,11,13,12)(16,17,18,19));