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C41×GL(2,𝔽3) #14520176

order1968
isoclinismisoclinic class of #226
automorphism?
homologyAbelianization (H1) = C2×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×GL(2,𝔽3)

Splittings

FittingQ8×C41 ⋊ D3
derivedSL(2,𝔽3) ⋊ C2×C41

Subgroups

subgroupG/H
center, socle, hypercenterC2×C41S4
commutator, cosocle, hypocenterSL(2,𝔽3)C2×C41
FrattiniC2S4×C41
FittingQ8×C41D3
LCSG ▷ SL(2,𝔽3)
UCSC1 ◁ C2×C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 328

A minimal faithful permutation representation — 2 generators on 49 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)(42,43,49,44,45,48,47,46);(43,46,49)(44,47,48)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 99);