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C5×#4455 #11746154

order960
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C4×C5×C8 · Schur multiplier (H2) = C4

Aliases

direct productC5×#4455

Splittings

HallC3×C5 ⋊ #322
SylowC3 ⋊ C5×#322

Subgroups

subgroupG/H
centerC42×C5C2×D3
commutatorC2×C3C4×C5×C8
FrattiniC42C2×C5×D3
FittingC3×C4×C5×C8C2
socle, prime radicalC22×C3×C5C42
cosocleC3×C42C22×C5
hypercenterC4×C5×C8D3
hypocenterC3C5×#322
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C42×C5 ◁ C4×C5×C8

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3,4,5)(6,7,8)(17,18,19,22,20,21,23,24);(7,8)(9,10,11,13,12,14,15,16)(18,21)(22,24)

Conjugacy classes & character table

360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×#67511, C5×#67512, #14277504, …
maximal normal subgroup ofC5×#67511, C5×#67512, #14277504, …
maximal quotient ofC5×C3⋊#1273, C5×#67438, C5×#67511, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 349);