Finite Group DatabasebetaFinite Group Databasebeta| order | 4374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C34 · Schur multiplier (H2) = C36 |
| direct product | C32×#92259 |
| Fitting, Sylow | C32×#6891 ⋊ C2 |
13768 conjugacy classes of subgroups; only the 752 normal subgroups are shown.
This group has 13768 conjugacy classes of subgroups — too many to draw. Only its 752 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) = 162 |
A minimal faithful permutation representation — 4 generators on 24 points:
(4,5,6)(8,10)(9,12)(11,13)(14,15);(7,8,14)(9,11,13)(10,12,15)(16,19,24,18,22,20,21,17,23);(1,2,3);(17,19,22)(20,24,23)378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72243516, C3⋊D3×#92259, C3×#72253805 |
| maximal normal subgroup of | #72243516, C3⋊D3×#92259, C3×#72253805 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((4,5,6)(8,10)(9,12)(11,13)(14,15), (7,8,14)(9,11,13)(10,12,15)(16,19,24,18,22,20,21,17,23), (1,2,3), (17,19,22)(20,24,23));