Finite Group Databasebeta

← Prev (#87787) Next (#87789) →

Cayley diagram

C5×#681 #87788

order400
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#681

Splittings

SylowC52 ⋊ M16

Subgroups

subgroupG/H
centerC4×C5C2×D5
commutatorC2×C5C2×C4×C5
FrattiniC4C2×C5×D5
FittingC2×C4×C52C2
socleC2×C52C2×C4
prime radicalC22×C52C4
cosocleC4×C5C22×C5
hypercenterC2×C4×C5D5
hypocenterC5C5×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C2×C4×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 40

A minimal faithful permutation representation — 2 generators on 18 points:

(1,2,3,4,5)(6,7,9,10,8)(12,15)(16,18);(7,8)(9,10)(11,15,13,18,14,12,17,16)

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716599, #11716600, #11716601, …
maximal normal subgroup of#11716599, #11716600, #11716601, …
maximal quotient ofC5×#3935, C5×C4⋊#168, C5×C22⋊#168, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 82);