Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #2898⋊C3 |
| Fitting, Sylow | #2898 ⋊ C3 |
191 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 2 generators on 36 points:
(6,11)(7,16)(8,9,19)(12,15)(13,24,27,23,14,35)(17,32,33,31,18,34)(20,22,21)(25,30,36,28,26,29);(1,2,3,4)(5,27)(6,21)(7,35)(8,30)(9,13)(10,29)(11,34)(12,33)(14,20)(15,19)(16,36)(17,26)(18,23)(22,28)(24,31)(25,32)Polycyclic presentation:
2^2,3,2^5|a^2=eh,d^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,d^b=dh,f^c=g,g^c=fg,g^f=gh52 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#2898⋊C3, #60086⋊C3, #60088⋊C3, … |
| maximal normal subgroup of | C2×#2898⋊C3, #60086⋊C3, #60088⋊C3, … |
| maximal quotient of | #17439⋊C3, #17518⋊C3, #17549⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5814);