Finite Group DatabasebetaFinite Group Databasebeta| order | 14400 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C22×C5 |
| direct product | A4×A4⋊#1044 |
| Fitting, socle | C24×C52 ⋊ C3×Dic3 |
| derived | C22×C52×A4 ⋊ C3×C4 |
| Sylow | C52 ⋊ A4×SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C22×C52×A4 | C3×C4 |
| Fitting, socle | C24×C52 | C3×Dic3 |
| prime radical | A42×C5⋊D5 | C2 |
| cosocle | C22×A4×C5⋊D5 | C2×C3 |
| LCS | G ▷ C22×C52×A4 | |
| UCS | C1 | |
912 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 18 points:
(2,4,3)(5,8,6,7)(10,11,12,13)(15,16,17,18);(1,4)(2,3)(6,7,8)(9,10,13,11,12)(14,15,16,18,17)136 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#72214019, #72260373, #72260445 |
| maximal normal subgroup of | A4×#72214019, #72260373, #72260445 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,4,3)(5,8,6,7)(10,11,12,13)(15,16,17,18), (1,4)(2,3)(6,7,8)(9,10,13,11,12)(14,15,16,18,17));