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C3×C5×C11×D21 #20294196

order6930
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×D21
unambiguous semidirect productC3⋊(C3×C5×C11×D7)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C2
derivedC3×C7 ⋊ C2×C3×C5×C11
HallC32×C7×C11 ⋊ C2×C5
HallC32×C5×C11 ⋊ D7
HallC5×C7×C11 ⋊ C3×D3
HallC32×C5×C7 ⋊ C2×C11
HallC32×C11 ⋊ C5×D7
HallC7×C11 ⋊ C3×C5×D3
HallC32×C7 ⋊ C2×C5×C11
HallC32×C5 ⋊ C11×D7
HallC5×C7 ⋊ C3×D3×C11
SylowC32 ⋊ C5×C11×D7
SylowC7 ⋊ C3×C5×D3×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11D21
commutator, hypocenterC3×C7C2×C3×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C7×C11C2
LCSG ▷ C3×C7
UCSC1 ◁ C3×C5×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D11×D21, C3×C5×D3×C11×D7, C3×C5×D21⋊D11, …
maximal normal subgroup ofC3×C5×D11×D21, C3×C5×D3×C11×D7, C3×C5×D21⋊D11, …
maximal quotient ofC3×C5×C11×Dic21, C2×C3×C5×C11×D21, C3×C11×C25×D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 83);