Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11925361 |
| Hall | C3×C52 ⋊ C2×C4⋊C4 |
| Sylow | C52 ⋊ C2×Dic3⋊C4 |
| Sylow | C3 ⋊ C2×#87832 |
476 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 93 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)(7,9)(10,11,13,12)(15,16,19,18);(1,2,3)(4,5);(6,7)(8,9)(11,12,13,14)(16,17,19,18)84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72224586, C2×#72224581, C2×D3×#87832, … |
| maximal normal subgroup of | C2×#72224586, C2×#72224581, C2×D3×#87832, … |
| maximal quotient of | C2×#72229361, #72259372, C2×#72224602 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,3)(7,9)(10,11,13,12)(15,16,19,18), (1,2,3)(4,5), (6,7)(8,9)(11,12,13,14)(16,17,19,18));