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C5×#4504 #11746203

order960
isoclinismisoclinic class of D48
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#4504

Splittings

HallC3×C5 ⋊ #366
SylowC3 ⋊ C5×#366

Subgroups

subgroupG/H
centerC22×C5D24
commutatorC3×C8C2×C4×C5
FrattiniC2×C8C2×C5×D3
FittingC2×C3×C5×C16C2
socle, prime radicalC22×C3×C5D8
cosocleC2×C3×C8C22×C5
hypercenterC2×C5×C16D3
hypocenterC3C5×#366
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C2×C5×C16

92 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)(13,14,19,25,16,20,23,26,17,21,27,28,22,24,15,18);(7,8)(9,10,11,12)(14,18)(15,19)(16,22)(20,28)(21,26)(23,27)(24,25)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#67824, C5×#67596, #14279572, …
maximal normal subgroup ofC5×#67824, C5×#67596, #14279572, …
maximal quotient ofC5×#67500, C5×#67806, C5×#67591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 398);