Finite Group Databasebeta

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C5×C7×C11×C3⋊D3 #20294202

order6930
isoclinismisoclinic class of C3⋊D3
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C11 · Schur multiplier (H2) = C3

Aliases

direct productC5×C7×C11×C3⋊D3
unambiguous semidirect productC3⋊(C5×D3×C7×C11)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C2
derived, SylowC32 ⋊ C2×C5×C7×C11
HallC32×C7×C11 ⋊ C2×C5
HallC32×C5×C11 ⋊ C2×C7
HallC32×C5×C7 ⋊ C2×C11
HallC32×C11 ⋊ C2×C5×C7
HallC32×C7 ⋊ C2×C5×C11
HallC32×C5 ⋊ C2×C7×C11

Subgroups

subgroupG/H
center, hypercenterC5×C7×C11C3⋊D3
commutator, hypocenterC32C2×C5×C7×C11
FrattiniC1G
Fitting, socleC32×C5×C7×C11C2
LCSG ▷ C32
UCSC1 ◁ C5×C7×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×C3⋊D3×D11, C5×C11×D7×C3⋊D3, C5×C3⋊D3×D77, …
maximal normal subgroup ofC5×C7×C3⋊D3×D11, C5×C11×D7×C3⋊D3, C5×C3⋊D3×D77, …
maximal quotient ofC5×C7×C11×C3⋊Dic3, C2×C5×C7×C11×C3⋊D3, C7×C11×C3⋊D3×C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 89);