Finite Group Databasebeta

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Cayley diagram

D5×#107 #65168

order320
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD5×#107

Splittings

FittingC5×#107 ⋊ C2
SylowC5 ⋊ C2×#107

Subgroups

subgroupG/H
centerC22D4×D5
commutatorC4×C5C22×C4
FrattiniC2×C4C22×D5
FittingC5×#107C2
socleC22×C5C2×D4
prime radicalC22×D5D4
cosocleC2×C4×C5C23
hypercenter#107D5
hypocenterC5C2×#107
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 160

A minimal faithful permutation representation — 3 generators on 17 points:

(5,6,10,12,8,11,7,9)(13,14,16,17,15);(1,2,3,4)(6,9)(7,10)(11,12);(14,15)(16,17)

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10598619, #10598622, D5×#357, …
maximal normal subgroup of#10598619, #10598622, D5×#357, …
maximal quotient ofD5×#335, #10599362, #10599365, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 506);