Finite Group Databasebeta

← Prev (#91965) Next (#91967) →

Cayley diagram

D5×#41⋊C3 #91966

order480
isoclinismisoclinic class of C5⋊(#41⋊C3)
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD5×#41⋊C3
unambiguous semidirect product(D5×#41)⋊C3

Splittings

FittingC5×#41 ⋊ C2×C3
HallD5×#41 ⋊ C3
SylowC5 ⋊ C2×#41⋊C3

Subgroups

subgroupG/H
center, hypercenterC4D5×A4
commutator, cosocle, hypocenterC5×Q8C22×C3
FrattiniC2C2×D5×A4
FittingC5×#41C2×C3
socleC2×C5C22×A4
LCSG ▷ C5×Q8
UCSC1 ◁ C4

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2,4,5,3)(6,7,10,13)(8,12,16,19,9,18,15,21,14,11,17,20);(2,3)(4,5)(6,14,10,16)(7,18,13,20)(8,17,15,9)(11,21,19,12)

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×GU(2,𝔽3), #11751624, D5×#131⋊C3, …
maximal normal subgroup ofD5×GU(2,𝔽3), #11751624, D5×#131⋊C3, …
maximal quotient ofC4×C5⋊(#41⋊C3), #65903⋊C3, C4×D5×SL(2,𝔽3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1042);