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C5×D13×D123 #44544436

order31980
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D13×D123
unambiguous semidirect product(C3×D13)⋊(C5×D41)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C22
derived, HallC3×C13×C41 ⋊ C22×C5
HallC5×C13×C41 ⋊ C2×D3
HallC3×C5×C41 ⋊ C2×D13
HallC13×C41 ⋊ C2×C5×D3
HallC5×C41 ⋊ D3×D13
HallC3×C5×C13 ⋊ C2×D41
HallC3×C41 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×D123
SylowC41 ⋊ C5×D3×D13
HallC3×C13 ⋊ C2×C5×D41
HallC3×C5 ⋊ D13×D41
SylowC13 ⋊ C2×C5×D123
SylowC3 ⋊ C5×D13×D41

Subgroups

subgroupG/H
center, hypercenterC5D13×D123
commutator, cosocle, hypocenterC3×C13×C41C22×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C41C22
LCSG ▷ C3×C13×C41
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 62
transitive degreeμt(G) = 7995

A minimal faithful permutation representation — 2 generators on 62 points:

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

Conjugacy classes & character table

2520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 164);