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C3×C72×C11⋊C5 #22549116

order8085
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C3×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC3×C72×C11⋊C5
unambiguous semidirect productC11⋊(C3×C5×C72)
unambiguous semidirect product(C3×C11)⋊(C5×C72)
unambiguous semidirect product(C3×C7×C11)⋊(C5×C7)
unambiguous semidirect product(C3×C72×C11)⋊C5

Splittings

Fitting, socle, HallC3×C72×C11 ⋊ C5
derived, SylowC11 ⋊ C3×C5×C72
HallC72×C11 ⋊ C3×C5
HallC3×C11 ⋊ C5×C72

Subgroups

subgroupG/H
center, hypercenterC3×C72C11⋊C5
commutator, hypocenterC11C3×C5×C72
FrattiniC1G
Fitting, socleC3×C72×C11C5
LCSG ▷ C11
UCSC1 ◁ C3×C72

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1029 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C72×AGL(1,𝔽11), C3×C7×C7⋊AGL(1,𝔽11), C3×C7×D7×C11⋊C5, …
maximal normal subgroup ofC3×C72×AGL(1,𝔽11), C3×C7×C7⋊AGL(1,𝔽11), C3×C7×D7×C11⋊C5, …
maximal quotient ofC2×C3×C72×C11⋊C5, C72×C9×C11⋊C5, C32×C72×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8085, 9);