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C3×C5×#688 #11925188

order1200
isoclinismisoclinic class of #686
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×#688

Splittings

FittingC3×C52×Q8 ⋊ C2
HallC3×C52 ⋊ SD16
SylowC52 ⋊ C3×SD16

Subgroups

subgroupG/H
centerC2×C3×C5C22⋊D5
commutator, cosocleC4×C5C22×C3×C5
FrattiniC4C2×C3×C5×D5
FittingC3×C52×Q8C2
socleC2×C3×C52D4
prime radicalC3×C5×D20C2
hypercenterC3×C5×Q8D5
hypocenterC5C3×C5×SD16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C5 ◁ C3×C4×C5 ◁ C3×C5×Q8

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 398);