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C41×(C2×D3)⋊C4 #14520136

order1968
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C2×C4×C41 · Schur multiplier (H2) = C22

Aliases

direct productC41×(C2×D3)⋊C4
unambiguous semidirect product(C2×D3)⋊(C4×C41)

Splittings

FittingC2×C3×C4×C41 ⋊ C2
HallC3×C41 ⋊ C22⋊C4
SylowC3 ⋊ C22⋊C4×C41

Subgroups

subgroupG/H
centerC22×C41C2×D3
commutatorC2×C3C2×C4×C41
FrattiniC22C2×D3×C41
FittingC2×C3×C4×C41C2
socleC22×C3×C41C22
prime radicalC22×D3×C41C2
cosocleC22×C3C22×C41
hypercenterC2×C4×C41D3
hypocenterC3C22⋊C4×C41
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C41 ◁ C2×C4×C41

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 984

A minimal faithful permutation representation — 2 generators on 52 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 59);