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C2×C13×#11715913 #34118477

order20202
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC2×C13×#11715913

Splittings

Fitting, socle, HallC2×C7×C13×C37 ⋊ C3
derived, HallC7×C37 ⋊ C2×C3×C13
HallC7×C13×C37 ⋊ C2×C3
HallC2×C13×C37 ⋊ ΓL(1,𝔽8)
HallC2×C7×C37 ⋊ C3×C13
HallC13×C37 ⋊ C2×ΓL(1,𝔽8)
HallC2×C7×C13 ⋊ C37⋊C3
HallC7×C13 ⋊ C2×C37⋊C3
HallC2×C37 ⋊ C13×ΓL(1,𝔽8)
SylowC37 ⋊ C2×C13×ΓL(1,𝔽8)
HallC2×C7 ⋊ C13×C37⋊C3
SylowC7 ⋊ C2×C13×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C13#11715913
commutator, cosocle, hypocenterC7×C37C2×C3×C13
FrattiniC1G
Fitting, socleC2×C7×C13×C37C3
LCSG ▷ C7×C37
UCSC1 ◁ C2×C13

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

Conjugacy classes & character table

2314 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20202, 7);