Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| isoclinism | isoclinic class of D5⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C3×D5⋊AGL(1,𝔽5) |
| Fitting, socle | C22×C3×C52 ⋊ C2×C4 |
| derived, Sylow | C52 ⋊ C23×C3×C4 |
| Hall | C3×C52 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C23×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52 | C2×C4 |
| prime radical | C22×C3×D52 | C2 |
| cosocle | C5⋊D5 | C24×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C3 | |
1052 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 310 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 — 4 generators on 17 points:
(1,2,3)(4,5,8,6,7)(9,10,13,12,11)(16,17);(5,6,7,8)(10,12,11,13);(14,15);(10,11)(12,13)168 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(4,5,8,6,7)(9,10,13,12,11)(16,17), (5,6,7,8)(10,12,11,13), (14,15), (10,11)(12,13));