Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#1020⋊AGL(1,𝔽5) |
| Fitting | C25×C5 ⋊ C4×D3 |
| derived | C5×C22⋊A4 ⋊ C22×C4 |
| Sylow | C5 ⋊ C2×#1020⋊C4 |
2644 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 2644 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,5,3,4)(6,7)(9,13,12)(10,11,14);(11,14)(13,15);(2,3,4,5)(8,9)(10,12)(11,13)(14,15)76 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#1020⋊C2, #72243472, #72243698, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#1020⋊C2, #72243472, #72243698, … |
| maximal quotient of | #72243698, #72243922, D5×#1020⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,5,3,4)(6,7)(9,13,12)(10,11,14), (11,14)(13,15), (2,3,4,5)(8,9)(10,12)(11,13)(14,15));