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C2×C5×D1551 #44526693

order31020
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1551
unambiguous semidirect product(C2×C3)⋊(C5×D517)
unambiguous semidirect product(C2×C47)⋊(C5×D33)

Splittings

Fitting, socleC2×C3×C5×C11×C47 ⋊ C2
derived, HallC3×C11×C47 ⋊ C22×C5
HallC3×C5×C11×C47 ⋊ C22
HallC5×C11×C47 ⋊ C2×D3
HallC3×C5×C47 ⋊ C2×D11
HallC11×C47 ⋊ C2×C5×D3
HallC5×C47 ⋊ C2×D33
HallC3×C5×C11 ⋊ C2×D47
HallC3×C47 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×D141
SylowC47 ⋊ C2×C5×D33
HallC3×C11 ⋊ C2×C5×D47
HallC3×C5 ⋊ C2×D517
SylowC11 ⋊ C2×C5×D141
SylowC3 ⋊ C2×C5×D517

Subgroups

subgroupG/H
center, hypercenterC2×C5D1551
commutator, cosocle, hypocenterC3×C11×C47C22×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C47C2
LCSG ▷ C3×C11×C47
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 68
transitive degreeμt(G) = 15510

A minimal faithful permutation representation — 2 generators on 68 points:

(4,5)(6,7,8,9,10)(12,13)(14,15)(16,17)(18,19)(20,21)(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)(61,62)(63,64)(65,66)(67,68);(1,2)(3,4,5)(11,12,14,16,18,20,21,19,17,15,13)(22,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24)

Conjugacy classes & character table

7770 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 96);