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C2×C37×#63271 #34118482

order20202
isoclinismisoclinic class of #63271
automorphism?
homologyAbelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1

Aliases

direct productC2×C37×#63271

Splittings

Fitting, socle, HallC2×C7×C13×C37 ⋊ C3
derived, HallC7×C13 ⋊ C2×C3×C37
HallC7×C13×C37 ⋊ C2×C3
HallC2×C13×C37 ⋊ ΓL(1,𝔽8)
HallC2×C7×C37 ⋊ C13⋊C3
HallC13×C37 ⋊ C2×ΓL(1,𝔽8)
HallC7×C37 ⋊ C2×C13⋊C3
HallC2×C7×C13 ⋊ C3×C37
HallC2×C13 ⋊ ΓL(1,𝔽8)×C37
HallC2×C7 ⋊ C37×C13⋊C3
SylowC13 ⋊ C2×ΓL(1,𝔽8)×C37
SylowC7 ⋊ C2×C37×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C37#63271
commutator, cosocle, hypocenterC7×C13C2×C3×C37
FrattiniC1G
Fitting, socleC2×C7×C13×C37C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 59
transitive degreeμt(G) = 6734

A minimal faithful permutation representation — 2 generators on 59 points:

(2,3,5)(4,7,10)(6,9,8)(11,13,12)(15,16,17)(18,20,19)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57)(58,59);(1,2,4,3,6,10,7,11,13,5,8,12,9)(14,15,17,19,16,18,20)

Conjugacy classes & character table

2442 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20202, 12);