Finite Group Databasebeta

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C3×C4×D5×C11 #13050397

order1320
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C11 · Schur multiplier (H2) = C2

Aliases

direct productC3×C4×D5×C11

Splittings

FittingC3×C4×C5×C11 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C4×C11
HallC3×C5×C11 ⋊ C2×C4
HallC5×C11 ⋊ C2×C3×C4
HallC3×C5 ⋊ C2×C4×C11

Subgroups

subgroupG/H
center, hypercenterC3×C4×C11D5
commutator, hypocenterC5C2×C3×C4×C11
FrattiniC2C2×C3×D5×C11
FittingC3×C4×C5×C11C2
socleC2×C3×C5×C11C22
prime radicalC2×C3×D5×C11C2
cosocleC2×C5C22×C3×C11
LCSG ▷ C5
UCSC1 ◁ C3×C4×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 101);