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C22×C3×C43⋊C7 #16813432

order3612
isoclinismisoclinic class of C43⋊C7
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22×C3×C43⋊C7
unambiguous semidirect product(C22×C3×C43)⋊C7

Splittings

Fitting, socle, HallC22×C3×C43 ⋊ C7
derived, SylowC43 ⋊ C22×C3×C7
HallC22×C43 ⋊ C3×C7
HallC3×C43 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC22×C3C43⋊C7
commutator, cosocle, hypocenterC43C22×C3×C7
FrattiniC1G
Fitting, socleC22×C3×C43C7
LCSG ▷ C43
UCSC1 ◁ C22×C3

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 516

A minimal faithful permutation representation — 2 generators on 50 points:

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

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×(C43⋊C7)⋊C9, C22⋊((C43⋊C7)⋊C9), C22⋊C9×C43⋊C7, …
maximal normal subgroup ofC22×(C43⋊C7)⋊C9, C22⋊((C43⋊C7)⋊C9), C22⋊C9×C43⋊C7, …
maximal quotient ofC22×C9×C43⋊C7, C2×C3×D3×C43⋊C7, C22×C32×C43⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3612, 44);