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C5×#63216 #13062637

order1360
isoclinismisoclinic class of #595
automorphism?
homologyAbelianization (H1) = C5×C16 · Schur multiplier (H2) = C1

Aliases

direct productC5×#63216

Splittings

derived, SylowC17 ⋊ C5×C16
HallC5×C17 ⋊ C16

Subgroups

subgroupG/H
center, hypercenterC4×C5#595
commutator, hypocenterC17C5×C16
FrattiniC4C5×#595
FittingC4×C5×C17C4
socle, prime radicalC2×C5×C17C8
cosocle#3622C2×C5
LCSG ▷ C17
UCSC1 ◁ C4×C5

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 1360

A minimal faithful permutation representation — 2 generators on 38 points:

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 5);