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C2×C5×C43⋊C3 #13046258

order1290
isoclinismisoclinic class of C43⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C43⋊C3
unambiguous semidirect product(C2×C43)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C43)⋊C3

Splittings

Fitting, socle, HallC2×C5×C43 ⋊ C3
derived, SylowC43 ⋊ C2×C3×C5
HallC5×C43 ⋊ C2×C3
HallC2×C43 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5C43⋊C3
commutator, cosocle, hypocenterC43C2×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C43C3
LCSG ▷ C43
UCSC1 ◁ C2×C5

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 430

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

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

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×(C43⋊C3)⋊C4, Dic5×C43⋊C3, (C43⋊C3)⋊Dic5, …
maximal normal subgroup ofC5×(C43⋊C3)⋊C4, Dic5×C43⋊C3, (C43⋊C3)⋊Dic5, …
maximal quotient ofC4×C5×C43⋊C3, C22×C5×C43⋊C3, C2×C5×C43⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1290, 4);