Finite Group Databasebeta

← Prev (#27190486) Next (#27190488) →

C2×C3×C17×C43⋊C3 #27190487

order13158
isoclinismisoclinic class of C43⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C17 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C17×C43⋊C3
unambiguous semidirect product(C2×C43)⋊(C32×C17)
unambiguous semidirect product(C2×C3×C43)⋊(C3×C17)
unambiguous semidirect product(C2×C17×C43)⋊C32
unambiguous semidirect product(C2×C3×C17×C43)⋊C3

Splittings

Fitting, socleC2×C3×C17×C43 ⋊ C3
derived, SylowC43 ⋊ C2×C32×C17
HallC2×C17×C43 ⋊ C32
HallC17×C43 ⋊ C2×C32
HallC2×C43 ⋊ C32×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17C43⋊C3
commutator, cosocle, hypocenterC43C2×C32×C17
FrattiniC1G
Fitting, socleC2×C3×C17×C43C3
LCSG ▷ C43
UCSC1 ◁ C2×C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 65
transitive degreeμt(G) = 4386

A minimal faithful permutation representation — 2 generators on 65 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,33)(18,26,31)(21,29,28)(23,32,25)(27,36,40)(30,37,39)(34,41,35)(38,42,43)(44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(64,65);(1,2,4,8,15,20,5,9,16,25,35,32,12,19,28,24,34,41,22,31,39,36,14,23,33,40,43,42,26,7,13,21,30,38,37,17,3,6,11,18,27,29,10)(61,62,63)

Conjugacy classes & character table

1734 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C17×(C43⋊C3)⋊C4, C3×(C43⋊C3)⋊Dic17, C3×Dic17×C43⋊C3, …
maximal normal subgroup ofC3×C17×(C43⋊C3)⋊C4, C3×(C43⋊C3)⋊Dic17, C3×Dic17×C43⋊C3, …
maximal quotient ofC3×C4×C17×C43⋊C3, C22×C3×C17×C43⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13158, 21);