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C2×C3×C7×D5×C31 #27189282

order13020
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D5×C31
unambiguous semidirect productC5⋊(C22×C3×C7×C31)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C7×C31)

Splittings

Fitting, socleC2×C3×C5×C7×C31 ⋊ C2
derived, SylowC5 ⋊ C22×C3×C7×C31
HallC3×C5×C7×C31 ⋊ C22
HallC5×C7×C31 ⋊ C22×C3
HallC3×C5×C31 ⋊ C22×C7
HallC5×C31 ⋊ C22×C3×C7
HallC3×C5×C7 ⋊ C22×C31
HallC5×C7 ⋊ C22×C3×C31
HallC3×C5 ⋊ C22×C7×C31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C31D5
commutator, cosocle, hypocenterC5C22×C3×C7×C31
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C31C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C7×C31

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 6510

A minimal faithful permutation representation — 2 generators on 48 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);(1,2,4,5,3)(47,48)

Conjugacy classes & character table

5208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 249);