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Cayley diagram

C2×Dic40 #65194

order320
isoclinismisoclinic class of D80
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic40

Splittings

SylowC5 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D40
commutator, cosocleC5×C8C23
FrattiniC8C22×D5
FittingC2×C5×C16C2
socle, prime radicalC22×C5D8
hypercenterC2×C16D5
hypocenterC5C2×Q32
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 320

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10598069, #10598075, #10598088, …
maximal normal subgroup of#10598069, #10598075, #10598088, …
maximal quotient of#10599837, C4×Dic40, #10599858, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 532);