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C32×C5×C11×D7 #20294188

order6930
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C11×D7

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C2
derived, SylowC7 ⋊ C2×C32×C5×C11
HallC32×C7×C11 ⋊ C2×C5
HallC5×C7×C11 ⋊ C2×C32
HallC32×C5×C7 ⋊ C2×C11
HallC7×C11 ⋊ C2×C32×C5
HallC32×C7 ⋊ C2×C5×C11
HallC5×C7 ⋊ C2×C32×C11

Subgroups

subgroupG/H
center, hypercenterC32×C5×C11D7
commutator, hypocenterC7C2×C32×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C7×C11C2
LCSG ▷ C7
UCSC1 ◁ C32×C5×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2475 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×D7×D11, C32×D5×C11×D7, C32×D7×D55, …
maximal normal subgroup ofC32×C5×D7×D11, C32×D5×C11×D7, C32×D7×D55, …
maximal quotient ofC32×C5×C11×Dic7, C2×C32×C5×C11×D7, C32×C11×D7×C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 75);