Finite Group Databasebeta

← Prev (#91147) Next (#91149) →

Cayley diagram

ΓL(1,𝔽16)⋊C8 #91148

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

Aliases

unambiguous semidirect productΓL(1,𝔽16)⋊C8

Splittings

derived, HallC3×C5 ⋊ C4×C8
SylowC5 ⋊ C8×Dic3
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:

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

Polycyclic presentation:

2^5,3,5|a^2=c,b^2=d,c^2=e,d^2=e,g^a=g^2,f^b=f^2,g^c=g^4

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C8×AGL(1,𝔽5), #11751650, #11751656, …
maximal normal subgroup ofD3×C8×AGL(1,𝔽5), #11751650, #11751656, …
maximal quotient ofΓL(1,𝔽16)⋊C16, #11746451, C3⋊C8×#170, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 224);