Finite Group Databasebeta

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C5×C3⋊((C11⋊Dic11)⋊C3) #36345017

order21780
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C11

Aliases

direct productC5×C3⋊((C11⋊Dic11)⋊C3)
unambiguous semidirect productC3⋊(C5×(C11⋊Dic11)⋊C3)
unambiguous semidirect product(C5×C3⋊(C11⋊Dic11))⋊C3

Splittings

derivedC3×C112 ⋊ C3×C4×C5
HallC3×C5×C112⋊C3 ⋊ C4
HallC3×C112⋊C3 ⋊ C4×C5
HallC5×C112 ⋊ C3×Dic3
SylowC112 ⋊ C3×C5×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊((C11⋊D11)⋊C3)
commutator, hypocenterC3×C112C3×C4×C5
FrattiniC2C5×C3⋊((C11⋊D11)⋊C3)
Fitting, socleC2×C3×C5×C112C2×C3
prime radicalC2×C3×C5×C112⋊C3C2
cosocleC2×C3×C112C2×C3×C5
LCSG ▷ C3×C112
UCSC1 ◁ C2×C5

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

690 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 366);