Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of D96 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1416 |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2)(8,9,13,17)(10,19,22,36)(11,23,25,39)(12,26,24,16)(14,27,29,18)(15,31,32,20)(21,38,34,30)(28,35,33,37);(2,3)(4,5,6,7)(9,14)(10,18)(11,20)(12,24)(15,30)(16,33)(17,29)(19,23)(21,37)(22,27)(25,31)(26,28)(32,38)(34,35)(36,39)Polycyclic presentation:
2^7,3|a^2=d,b^2=g,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×#1416, C2×#67597, #10715618, … |
| maximal normal subgroup of | D3×#1416, C2×#67597, #10715618, … |
| maximal quotient of | #10682641, #10682746, #10682824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 173);