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C5×#66493 #13109980

order1640
isoclinismisoclinic class of #4223
automorphism?
homologyAbelianization (H1) = C5×C8 · Schur multiplier (H2) = C1

Aliases

direct productC5×#66493

Splittings

derived, SylowC41 ⋊ C5×C8
HallC5×C41 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC2×C5#4223
commutator, hypocenterC41C5×C8
FrattiniC2C5×#4223
Fitting, socle, prime radicalC2×C5×C41C4
cosocleDic41C2×C5
LCSG ▷ C41
UCSC1 ◁ C2×C5

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 54
transitive degreeμt(G) = 1640

A minimal faithful permutation representation — 2 generators on 54 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1640, 16);