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D5×#13049955 #27189176

order13020
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD5×#13049955

Splittings

Fitting, socle, derived, HallC5×C7×C31 ⋊ C22×C3
HallC7×D5×D31 ⋊ C3
HallC5×#10620253 ⋊ C22
Hall#10620253 ⋊ C2×D5
HallD5×D31 ⋊ ΓL(1,𝔽8)
HallC7×C31 ⋊ C2×C3×D5
HallC5×C31 ⋊ C22×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×D31⋊C3
SylowC31 ⋊ C2×D5×ΓL(1,𝔽8)
SylowC7 ⋊ D5×D31⋊C3
SylowC5 ⋊ C2×#13049955

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C31C22×C3
LCSG ▷ C5×C7×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 1085

A minimal faithful permutation representation — 2 generators on 43 points:

(2,6,7,3,4,8)(5,14,15,9,10,22)(11,25,26,17,18,30)(12,24,20,19,16,13)(21,23,31,27,28,29)(33,34,35)(36,38,37)(39,40,42,43,41);(1,2,5,11,19,4,8,13,21,28,10,16,22,26,31,18,25,29,30,15,24,14,23,27,20,7,6,12,17,9,3)(32,33,35,37,34,36,38)(40,41)(42,43)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 143);