Finite Group Databasebeta

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Cayley diagram

C4×C22⋊Dic5 #65498

order320
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×C22⋊Dic5

Splittings

SylowC5 ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D5
commutatorC2×C5C2×C42
FrattiniC23C22×D5
FittingC23×C4×C5C2
socle, cosocleC23×C5C23
prime radicalC24×C5C22
hypercenterC23×C4D5
hypocenterC5C4×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C23×C4

258 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:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10598109, #10598119, #10598168, …
maximal normal subgroup of#10598109, #10598119, #10598168, …
maximal quotient ofC4×C22⋊#168, #10602322, C4×#3963, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 836);