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C3×#64665 #11745810

order960
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C64 · Schur multiplier (H2) = C1

Aliases

direct productC3×#64665

Splittings

derived, SylowC5 ⋊ C3×C64
HallC3×C5 ⋊ C64

Subgroups

subgroupG/H
center, hypercenterC3×C16AGL(1,𝔽5)
commutator, hypocenterC5C3×C64
FrattiniC16C3×AGL(1,𝔽5)
FittingC3×C5×C16C4
socle, prime radicalC2×C3×C5C32
cosocle#3926C2×C3
LCSG ▷ C5
UCSC1 ◁ C3×C16

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 72
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 2 generators on 72 points:

(1,2,3)(5,6,7,8)(9,10,11,16,12,17,21,31,13,18,22,32,25,35,41,51,14,19,23,33,26,36,42,52,28,38,44,54,47,57,61,66,15,20,24,34,27,37,43,53,29,39,45,55,48,58,62,67,30,40,46,56,49,59,63,68,50,60,64,69,65,70,71,72);(4,5,6,8,7)

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×#64665, C3×D5⋊C64, D3×#64665, …
maximal normal subgroup ofC2×C3×#64665, C3×D5⋊C64, D3×#64665, …
maximal quotient ofC3×#10597921, C2×C3×#64665

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 5);