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C32×C4×C43⋊C7 #24925502

order10836
isoclinismisoclinic class of C43⋊C7
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C4×C43⋊C7
unambiguous semidirect product(C32×C4×C43)⋊C7

Splittings

Fitting, HallC32×C4×C43 ⋊ C7
derived, SylowC43 ⋊ C32×C4×C7
HallC32×C43 ⋊ C4×C7
HallC4×C43 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC32×C4C43⋊C7
commutator, hypocenterC43C32×C4×C7
FrattiniC2C2×C32×C43⋊C7
FittingC32×C4×C43C7
socleC2×C32×C43C2×C7
prime radicalC2×C32×C43⋊C7C2
cosocleC2×C43C2×C32×C7
LCSG ▷ C43
UCSC1 ◁ C32×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

468 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 94);