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C3×C37×D91 #34118490

order20202
isoclinismisoclinic class of D91
automorphism?
homologyAbelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1

Aliases

direct productC3×C37×D91

Splittings

Fitting, socle, HallC3×C7×C13×C37 ⋊ C2
derived, HallC7×C13 ⋊ C2×C3×C37
HallC7×C13×C37 ⋊ C2×C3
HallC3×C13×C37 ⋊ D7
HallC3×C7×C37 ⋊ D13
HallC13×C37 ⋊ C3×D7
HallC3×C7×C13 ⋊ C2×C37
HallC7×C37 ⋊ C3×D13
HallC3×C13 ⋊ D7×C37
HallC3×C7 ⋊ D13×C37
SylowC13 ⋊ C3×D7×C37
SylowC7 ⋊ C3×D13×C37

Subgroups

subgroupG/H
center, hypercenterC3×C37D91
commutator, cosocle, hypocenterC7×C13C2×C3×C37
FrattiniC1G
Fitting, socleC3×C7×C13×C37C2
LCSG ▷ C7×C13
UCSC1 ◁ C3×C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 60
transitive degreeμt(G) = 10101

A minimal faithful permutation representation — 2 generators on 60 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16)(17,18)(19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57)(58,59,60);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,17,19,20,18,16)

Conjugacy classes & character table

5217 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20202, 20);