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Cayley diagram

C2×C5×C22⋊A4 #92133

order480
isoclinismisoclinic class of C22⋊A4
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C24

Aliases

direct productC2×C5×C22⋊A4

Splittings

Fitting, socle, HallC25×C5 ⋊ C3
derivedC24 ⋊ C2×C3×C5
SylowC25 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5C22⋊A4
commutator, cosocle, hypocenterC24C2×C3×C5
FrattiniC1G
Fitting, socleC25×C5C3
LCSG ▷ C24
UCSC1 ◁ C2×C5

296 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 15
transitive degreeμt(G) = 60

A minimal faithful permutation representation — 3 generators on 15 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

derived subgroup of#14511887, #14511890, #14511892, …
maximal subgroup of#65536⋊C3, C5×#379⋊C3, C2×C5⋊(#120⋊C3), …
maximal normal subgroup of#65536⋊C3, C5×#379⋊C3, C2×C5⋊(#120⋊C3), …
maximal quotient ofC4×C5×C22⋊A4, C2×C5×C22⋊SL(2,𝔽3), C5×#5948, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1209);