Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×M64 ⋊ C2 |
| Sylow | C3 ⋊ #1419 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2)(5,11)(6,17)(7,9)(8,24)(12,30)(13,33)(14,32)(15,16)(18,25)(19,29)(20,22)(21,35)(23,28)(26,27)(31,34);(2,3)(4,5,7,13,10,15,9,26)(6,16,19,33,22,11,21,27)(8,23,18,30,25,31,24,14)(12,29,28,17,32,35,34,20)Polycyclic presentation:
2^7,3|a^2=d,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1419, C2×#67604, #10715662, … |
| maximal normal subgroup of | D3×#1419, C2×#67604, #10715662, … |
| maximal quotient of | #10682644, #10682749, #10682821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 180);