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C3×C5×C43⋊C7 #17985258

order4515
isoclinismisoclinic class of C43⋊C7
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C43⋊C7
unambiguous semidirect product(C3×C43)⋊(C5×C7)
unambiguous semidirect product(C3×C5×C43)⋊C7

Splittings

Fitting, socle, HallC3×C5×C43 ⋊ C7
derived, SylowC43 ⋊ C3×C5×C7
HallC5×C43 ⋊ C3×C7
HallC3×C43 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C5C43⋊C7
commutator, cosocle, hypocenterC43C3×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C43C7
LCSG ▷ C43
UCSC1 ◁ C3×C5

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 51
transitive degreeμt(G) = 645

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3)(4,5,6,7,8)(10,11,13,17,22,30,43)(12,15,19,26,37,48,14)(16,21,28,41,18,24,33)(20,25,35,46,29,40,51)(23,32,45,42,31,27,39)(34,44,36,47,38,49,50);(9,10,12,16,13,18,25,36,19,27,40,30,28,42,32,45,22,31,44,41,33,43,48,51,46,39,50,26,38,47,49,35,37,24,34,17,23,21,29,15,20,11,14)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C9×C43⋊C7, C5×(C43⋊C7)⋊C9, C3×C5×(C43⋊C3)⋊C7, …
maximal normal subgroup ofC5×C9×C43⋊C7, C5×(C43⋊C7)⋊C9, C3×C5×(C43⋊C3)⋊C7, …
maximal quotient ofC5×C9×C43⋊C7, C32×C5×C43⋊C7, C5×A4×C43⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4515, 2);