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C5×#4502 #11746201

order960
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C4×C5×C8 · Schur multiplier (H2) = C2

Aliases

direct productC5×#4502

Splittings

HallC3×C5 ⋊ #346
SylowC3 ⋊ C5×#346

Subgroups

subgroupG/H
centerC2×C5×C8C2×D3
commutatorC2×C3C4×C5×C8
FrattiniC2×C8C2×C5×D3
FittingC2×C3×C5×C16C2
socle, prime radicalC22×C3×C5C2×C8
cosocleC2×C3×C8C22×C5
hypercenterC2×C5×C16D3
hypocenterC3C5×#346
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5×C8 ◁ C2×C5×C16

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,3,4,5)(6,7,8)(13,14,15,19,16,20,21,26,17,18,22,24,23,25,27,28);(7,8)(9,10,11,12)(14,18)(19,24)(20,25)(26,28)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#67600, #14279234, C5×D3×#346, …
maximal normal subgroup ofC5×#67600, #14279234, C5×D3×#346, …
maximal quotient ofC5×#67498, C5×#67499, C5×#67804, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 396);