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C5×D96 #11746147

order960
isoclinismisoclinic class of D96
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D96

Splittings

FittingC3×C5×C32 ⋊ C2
HallC3×C5 ⋊ D32
SylowC3 ⋊ C5×D32

Subgroups

subgroupG/H
centerC2×C5D48
commutator, cosocleC3×C16C22×C5
FrattiniC16C2×C5×D3
FittingC3×C5×C32C2
socleC2×C3×C5D16
hypercenterC5×C32D3
hypocenterC3C5×D32
LCSG ▷ C3×C16 ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×C16 ◁ C5×C32

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,40);(7,37)(8,36)(9,35)(10,34)(11,33)(12,32)(13,31)(14,30)(15,29)(16,28)(17,27)(18,26)(19,25)(20,24)(21,23)(39,40)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#67607, C5×D192, #14279811, …
maximal normal subgroup ofC5×#67607, C5×D192, #14279811, …
maximal quotient ofC5×#67596, C5×#67591, C5×D192, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 342);