Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C5 |
| direct product | C3×#11717273 |
| Fitting | C24×C3×C52 ⋊ C2 |
| Hall | C3×C52 ⋊ #120 |
| Sylow | C52 ⋊ C3×#120 |
1040 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 262 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 600 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3)(9,10,12,13,11)(19,21);(4,5,7,8,6)(15,17);(5,6)(7,8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)618 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#120×C5⋊D5 |
| maximal normal subgroup of | C3×#120×C5⋊D5 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(9,10,12,13,11)(19,21), (4,5,7,8,6)(15,17), (5,6)(7,8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21));