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C2×C5×D1599 #44544496

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

Aliases

direct productC2×C5×D1599
unambiguous semidirect product(C2×C3)⋊(C5×D533)
unambiguous semidirect product(C2×C13)⋊(C5×D123)

Splittings

Fitting, socleC2×C3×C5×C13×C41 ⋊ C2
derived, HallC3×C13×C41 ⋊ C22×C5
HallC3×C5×C13×C41 ⋊ C22
HallC5×C13×C41 ⋊ C2×D3
HallC3×C5×C41 ⋊ C2×D13
HallC13×C41 ⋊ C2×C5×D3
HallC5×C41 ⋊ C2×D39
HallC3×C5×C13 ⋊ C2×D41
HallC3×C41 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×D123
SylowC41 ⋊ C2×C5×D39
HallC3×C13 ⋊ C2×C5×D41
HallC3×C5 ⋊ C2×D533
SylowC13 ⋊ C2×C5×D123
SylowC3 ⋊ C2×C5×D533

Subgroups

subgroupG/H
center, hypercenterC2×C5D1599
commutator, cosocle, hypocenterC3×C13×C41C22×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C41C2
LCSG ▷ C3×C13×C41
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 64
transitive degreeμt(G) = 15990

A minimal faithful permutation representation — 2 generators on 64 points:

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

Conjugacy classes & character table

8010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 224);