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Cayley diagram

C2×C5×GL(2,𝔽3) #91941

order480
isoclinismisoclinic class of #226
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×GL(2,𝔽3)

Splittings

FittingC2×C5×Q8 ⋊ D3
derivedSL(2,𝔽3) ⋊ C22×C5

Subgroups

subgroupG/H
center, socle, hypercenterC22×C5S4
commutator, cosocle, hypocenterSL(2,𝔽3)C22×C5
FrattiniC2C2×C5×S4
FittingC2×C5×Q8D3
LCSG ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C5

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 15
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 2 generators on 15 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11751599, #11751600, #11751601, …
maximal normal subgroup of#11751599, #11751600, #11751601, …
maximal quotient ofC5×#5386, C4×C5×GL(2,𝔽3), C5×C4⋊GL(2,𝔽3), …
automorphism group ofC32×C11, C2×C32×C11
outer automorphism group ofC32×C11, C2×C32×C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1017);