Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×#11925150 |
| derived | C3×C52 ⋊ C2×C3×C8 |
| Hall | C32×C52 ⋊ C2×C8 |
| Sylow | C52 ⋊ C2×C3×C3⋊C8 |
| Sylow | C32 ⋊ #87767 |
304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,6)(16,17)(18,19)(20,21)(22,23);(5,6)(7,8,9,11,10,12,13,14)(15,16,18,19,17)(21,22)(23,24)360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#72229661, #72259958, #72259968, … |
| maximal normal subgroup of | C3×#72229661, #72259958, #72259968, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(4,5,6)(16,17)(18,19)(20,21)(22,23), (5,6)(7,8,9,11,10,12,13,14)(15,16,18,19,17)(21,22)(23,24));