Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#441 ⋊ C2 |
| Sylow | C3 ⋊ #3127 |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3)(4,6,7,10)(5,9,8,11)(14,24)(18,22)(23,39)(25,41)(32,36)(33,37)(38,43)(40,42);(12,15,16,27)(13,19,20,34)(14,23,24,39)(17,31,29,28)(18,32,22,36)(21,35,30,26)(25,42,41,40)(33,38,37,43);(2,3)(5,8)(9,11)(12,14)(13,18)(15,23)(16,24)(17,25)(19,32)(20,22)(21,33)(26,43)(27,39)(28,40)(29,41)(30,37)(31,42)(34,36)(35,38);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13,16,20)(14,22,24,18)(15,26,27,35)(17,30,29,21)(19,31,34,28)(23,38,39,43)(25,33,41,37)(32,40,36,42)Polycyclic presentation:
2^7,3|a^2=g,c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,d^b=dg,h^b=h^2,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3127, C2×#79836, #11663557, … |
| maximal normal subgroup of | D3×#3127, C2×#79836, #11663557, … |
| maximal quotient of | #10795286, #10798291, #10798297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12412);