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C5×C7×C3⋊D33 #20294203

order6930
isoclinismisoclinic class of C3⋊D33
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC5×C7×C3⋊D33
unambiguous semidirect productC3⋊(C5×C7×D33)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C2
derived, HallC32×C11 ⋊ C2×C5×C7
HallC32×C7×C11 ⋊ C2×C5
HallC32×C5×C11 ⋊ C2×C7
HallC5×C7×C11 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ D11
HallC7×C11 ⋊ C5×C3⋊D3
HallC32×C7 ⋊ C5×D11
HallC5×C11 ⋊ C7×C3⋊D3
HallC32×C5 ⋊ C7×D11
SylowC11 ⋊ C5×C7×C3⋊D3
SylowC32 ⋊ C5×C7×D11

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊D33
commutator, hypocenterC32×C11C2×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C11C2
LCSG ▷ C32×C11
UCSC1 ◁ C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1785 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×C3⋊D3×D11, C5×D7×C3⋊D33, C5×D77⋊(C3⋊D3), …
maximal normal subgroup ofC5×C7×C3⋊D3×D11, C5×D7×C3⋊D33, C5×D77⋊(C3⋊D3), …
maximal quotient ofC5×C7×C3⋊Dic33, C2×C5×C7×C3⋊D33, C7×C25×C3⋊D33, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 90);