Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ #2143 |
220 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(6,16)(11,26)(15,31)(17,33)(18,25)(20,35)(27,28)(29,32);(2,3)(4,6)(5,11)(7,20)(8,18)(9,25)(10,16)(12,29)(13,27)(14,26)(15,19)(17,22)(21,33)(23,35)(24,28)(30,32)(31,34);(2,3)(4,5,8,13,10,14,9,24)(6,15,18,32,16,31,25,29)(7,19,21,30,23,34,22,12)(11,20,27,33,26,35,28,17)Polycyclic presentation:
2^7,3|a^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2,c^b=cg,d^b=df,f^b=fg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10710470, #10710473, #10710484, … |
| maximal normal subgroup of | #10710470, #10710473, #10710484, … |
| maximal quotient of | #10704933, #10704937, #10704941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4024);