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Cayley diagram

D5×C22⋊A4 #92127

order480
isoclinismisoclinic class of D5×C22⋊A4
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C24

Aliases

direct productD5×C22⋊A4
unambiguous semidirect productC5⋊(C2×C22⋊A4)

Splittings

Fitting, socle, derivedC24×C5 ⋊ C2×C3
HallC24×D5 ⋊ C3
SylowC5 ⋊ C2×C22⋊A4

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC24×C5C2×C3
LCSG ▷ C24×C5
UCSC1

296 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 13
transitive degreeμt(G) = 60

A minimal faithful permutation representation — 3 generators on 13 points:

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

Conjugacy classes & character table

32 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#65800⋊C3, D5×#120⋊C3, #11757174, …
maximal normal subgroup of#65800⋊C3, D5×#120⋊C3, #11757174, …
maximal quotient ofC5⋊#5948, D5×C22⋊SL(2,𝔽3), C5⋊#5950, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1203);