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Cayley diagram

C23×C5×A4 #92132

order480
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C24

Aliases

direct productC23×C5×A4

Splittings

Fitting, socle, HallC25×C5 ⋊ C3
derivedC22 ⋊ C23×C3×C5
SylowC25 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC23×C5A4
commutator, cosocle, hypocenterC22C23×C3×C5
FrattiniC1G
Fitting, socleC25×C5C3
LCSG ▷ C22
UCSC1 ◁ C23×C5

356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 15
transitive degreeμt(G) = 120

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

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#5432, #11752151, A4×C22⋊Dic5, …
maximal normal subgroup ofC5×#5432, #11752151, A4×C22⋊Dic5, …
maximal quotient ofC22×C4×C5×A4, C2×C5×D4×A4, C23×C5×SL(2,𝔽3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1208);