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.
| Fitting | C2×C3×C32 ⋊ C2 |
| Sylow | C3 ⋊ #1417 |
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:
(1,2)(4,6)(5,11)(7,24)(8,19)(9,31)(10,22)(12,38)(13,34)(14,43)(15,45)(16,36)(17,23)(18,27)(20,25)(21,29)(26,57)(28,59)(30,35)(32,50)(33,37)(39,51)(40,66)(41,65)(42,63)(44,67)(46,54)(47,56)(48,64)(49,62)(52,60)(53,55)(58,61);(2,3)(4,5,8,13,10,16,29,15)(6,17,19,46,22,47,21,53)(7,23,26,54,28,56,61,55)(9,30,25,14,32,42,60,44)(11,33,34,49,36,48,45,18)(12,37,39,62,41,64,40,27)(20,51,50,65,52,66,31,38)(24,43,57,63,59,67,58,35)Polycyclic presentation:
2^7,3|a^2=d,c^2=ef,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=ce,e^b=ef,f^b=fg,h^b=h^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1417, C2×#67598, #10715640, … |
| maximal normal subgroup of | D3×#1417, C2×#67598, #10715640, … |
| maximal quotient of | #10682638, #10682641, #10682749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 174);