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Cayley diagram

C3×(C2×AGL(1,𝔽5))⋊C4 #91210

order480
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C23

Aliases

direct productC3×(C2×AGL(1,𝔽5))⋊C4
unambiguous semidirect product(C2×AGL(1,𝔽5))⋊(C3×C4)

Splittings

FittingC2×C3×C4×C5 ⋊ C4
HallC3×C5 ⋊ #95
SylowC5 ⋊ C3×#95

Subgroups

subgroupG/H
centerC22×C3C2×AGL(1,𝔽5)
commutatorC2×C5C3×C42
FrattiniC22C2×C3×AGL(1,𝔽5)
FittingC2×C3×C4×C5C4
socleC22×C3×C5C2×C4
prime radicalC22×C3×D5C22
cosocleC22×D5C22×C3
hypercenterC2×C3×C4AGL(1,𝔽5)
hypocenterC5C3×#95
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 2 generators on 16 points:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746496, #11746497, #11746502, …
maximal normal subgroup of#11746496, #11746497, #11746502, …
maximal quotient ofC3×#64862, C3×#64863, C3×#64866, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 286);