Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C3×C32 ⋊ C2 |
| Sylow | C3 ⋊ #1401 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 67 points:
(2,3)(4,6)(5,12)(7,23)(8,26)(9,21)(10,19)(11,22)(13,36)(14,39)(15,34)(16,18)(17,35)(20,29)(24,47)(25,51)(27,54)(28,32)(30,48)(31,50)(33,42)(37,45)(38,60)(40,62)(41,53)(43,46)(44,59)(49,56)(52,66)(55,57)(58,64)(61,65)(63,67);(1,2,3)(4,5,8,14,9,15,27,40,10,16,28,41,30,43,55,63,11,17,29,42,31,44,56,64,7,13,24,37,25,38,52,61)(6,18,20,45,21,46,49,65,19,35,47,39,48,59,66,62,22,36,26,53,50,60,54,67,23,12,32,33,51,34,57,58)Polycyclic presentation:
2^7,3|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^b=cg,d^b=dg,h^b=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1401, C2×#67595, #10715396, … |
| maximal normal subgroup of | D3×#1401, C2×#67595, #10715396, … |
| maximal quotient of | #10682527, #10682587, #10682626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 171);