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C3×C43⋊C7 #11744745

order903
isoclinismisoclinic class of C43⋊C7
automorphism?
homologyAbelianization (H1) = C3×C7 · Schur multiplier (H2) = C1

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3C43⋊C7
commutator, cosocle, hypocenterC43C3×C7
FrattiniC1G
Fitting, socleC3×C43C7
LCSG ▷ C43
UCSC1 ◁ C3

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 129

A minimal faithful permutation representation — 2 generators on 46 points:

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

Conjugacy classes & character table

39 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D43⋊C7, D3×C43⋊C7, C3⋊(D43⋊C7), …
maximal normal subgroup ofC3×D43⋊C7, D3×C43⋊C7, C3⋊(D43⋊C7), …
maximal quotient ofC2×C3×C43⋊C7, C9×C43⋊C7, C32×C43⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(903, 2);