Finite Group Databasebeta

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C5×#6657 #11925085

order1200
isoclinismisoclinic class of #6653
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#6657

Splittings

HallC3×C52 ⋊ SD16
SylowC52 ⋊ #214
SylowC3 ⋊ C5×#677

Subgroups

subgroupG/H
centerC2×C5#1202
commutator, cosocleC3×C4×C5C22×C5
FrattiniC4C5×D3×D5
FittingC3×C4×C52C22
socleC2×C3×C52D4
prime radicalC3×C5×D20C2
hypercenterC4×C5D3×D5
hypocenterC3×C5C5×SD16
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C5 ◁ C4×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 295);