Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D5×AGL(1,𝔽5)×S4 |
| Fitting, socle | C22×C52 ⋊ C2×C4×D3 |
| derived | C52×A4 ⋊ C22×C4 |
| Sylow | C52 ⋊ C2×C4×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C52×A4 | C22×C4 |
| Fitting, socle | C22×C52 | C2×C4×D3 |
| prime radical | D52×S4 | C2 |
| cosocle | C5×D5×A4 | C23 |
| LCS | G ▷ C52×A4 | |
| UCS | C1 | |
965 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 965 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,3,2)(6,7)(8,9)(10,11)(12,13);(3,4)(5,8,7,6,9);(11,12,13,14)100 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1020⋊AGL(1,𝔽5) |
| maximal quotient of | D5×#1020⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,3,2)(6,7)(8,9)(10,11)(12,13), (3,4)(5,8,7,6,9), (11,12,13,14));