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C32×C7×D55 #20294191

order6930
isoclinismisoclinic class of D55
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×D55
unambiguous semidirect productC5⋊(C32×C7×D11)
unambiguous semidirect productC11⋊(C32×C7×D5)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C2
derived, HallC5×C11 ⋊ C2×C32×C7
HallC32×C7×C11 ⋊ D5
HallC32×C5×C11 ⋊ C2×C7
HallC5×C7×C11 ⋊ C2×C32
HallC32×C5×C7 ⋊ D11
HallC32×C11 ⋊ C7×D5
HallC7×C11 ⋊ C32×D5
HallC32×C5 ⋊ C7×D11
HallC5×C7 ⋊ C32×D11
SylowC11 ⋊ C32×C7×D5
SylowC5 ⋊ C32×C7×D11

Subgroups

subgroupG/H
center, hypercenterC32×C7D55
commutator, hypocenterC5×C11C2×C32×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C11C2
LCSG ▷ C5×C11
UCSC1 ◁ C32×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1827 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C7×D5×D11, C32×D7×D55, C32×D35⋊D11, …
maximal normal subgroup ofC32×C7×D5×D11, C32×D7×D55, C32×D35⋊D11, …
maximal quotient ofC32×C7×Dic55, C2×C32×C7×D55, C32×C7×D275, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 78);