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Cayley diagram

AGL(1,𝔽5)×C3⋊C8 #91147

order480
isoclinismisoclinic class of D3×AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C8 · Schur multiplier (H2) = C4

Aliases

direct productAGL(1,𝔽5)×C3⋊C8
unambiguous semidirect product(C3×AGL(1,𝔽5))⋊C8

Splittings

derived, HallC3×C5 ⋊ C4×C8
SylowC5 ⋊ C4×C3⋊C8
SylowC3 ⋊ C8×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC4D3×AGL(1,𝔽5)
commutator, hypocenterC3×C5C4×C8
FittingC3×C4×C5C2×C4
socleC2×C3×C5C42
prime radicalC2×C3×D5C2×C4
cosocleC3×C4×D5C22
LCSG ▷ C3×C5
UCSC1 ◁ C4

88 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:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C8×AGL(1,𝔽5), AGL(1,𝔽5)×ΓL(1,𝔽25), #11751656, …
maximal normal subgroup ofD3×C8×AGL(1,𝔽5), AGL(1,𝔽5)×ΓL(1,𝔽25), #11751656, …
maximal quotient ofAGL(1,𝔽5)×C3⋊C16, #11746450, C3⋊C8×#170, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 223);