Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of D96 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C32 ⋊ C2 |
| Sylow | C3 ⋊ #1415 |
82 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2)(9,14)(10,19)(11,20)(12,24)(15,16)(17,33)(18,29)(21,38)(22,36)(23,27)(25,37)(26,28)(30,39)(31,32)(34,35);(2,3)(4,5,6,7)(8,9)(10,14)(11,23)(12,26)(13,18)(15,19)(16,20)(17,24)(21,33)(22,29)(25,39)(27,35)(28,34)(30,38)(31,36)(32,37)Polycyclic presentation:
2^7,3|a^2=d,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,c^b=ce,e^b=ef,f^b=fg,h^b=h^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1415, C2×#67596, #10715620, … |
| maximal normal subgroup of | D3×#1415, C2×#67596, #10715620, … |
| maximal quotient of | #10682638, #10682743, #10682821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 172);