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C3×C7×D13×C37 #34118486

order20202
isoclinismisoclinic class of D13
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C37 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D13×C37

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C7×C37D13
commutator, cosocle, hypocenterC13C2×C3×C7×C37
FrattiniC1G
Fitting, socleC3×C7×C13×C37C2
LCSG ▷ C13
UCSC1 ◁ C3×C7×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)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50)(51,52,53,54,55,56,57)(58,59,60);(1,2,4,6,8,10,12,13,11,9,7,5,3)

Conjugacy classes & character table

6216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20202, 16);