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C3×C7×C151⋊C3 #23748885

order9513
isoclinismisoclinic class of C151⋊C3
automorphism?
homologyAbelianization (H1) = C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×C151⋊C3
unambiguous semidirect productC151⋊(C32×C7)
unambiguous semidirect product(C3×C151)⋊(C3×C7)

Splittings

Fitting, socleC3×C7×C151 ⋊ C3
derived, SylowC151 ⋊ C32×C7
HallC7×C151 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C7C151⋊C3
commutator, cosocle, hypocenterC151C32×C7
FrattiniC1G
Fitting, socleC3×C7×C151C3
LCSG ▷ C151
UCSC1 ◁ C3×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1113 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×D151⋊C3, C3×(C151⋊C3)⋊D7, C3×D7×C151⋊C3, …
maximal normal subgroup ofC3×C7×D151⋊C3, C3×(C151⋊C3)⋊D7, C3×D7×C151⋊C3, …
maximal quotient ofC2×C3×C7×C151⋊C3, C7×A4×C151⋊C3, C3×C7×C22⋊(C151⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9513, 11);