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Cayley diagram

#4150⋊C3 #91967

order480
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product#4150⋊C3

Splittings

FittingC5×#41 ⋊ C2×C3
Hall#4150 ⋊ C3
SylowC5 ⋊ 2−1+4⋊C3

Subgroups

subgroupG/H
center, FrattiniC2C2×D5×A4
commutator, cosocle, hypocenterC5×Q8C22×C3
FittingC5×#41C2×C3
socleC2×C5C22×A4
hypercenterC4D5×A4
LCSG ▷ C5×Q8
UCSC1 ◁ C2 ◁ C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2,4,5,3)(6,7,10,11)(8,20,17,18,14,13,15,21,9,12,16,19);(2,3)(4,5)(6,16,10,14)(7,20,11,21)(8,9,15,17)(12,19,18,13)

Polycyclic presentation:

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

Conjugacy classes & character table

47 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11751625, #11751626, #11751627, …
maximal normal subgroup of#11751625, #11751626, #11751627, …
maximal quotient of#65904⋊C3, SL(2,𝔽3)×D20, #65906⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1043);