Finite Group Databasebeta

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C4×C29×C43⋊C7 #46853574

order34916
automorphism?
homologyAbelianization (H1) = C4×C7×C29 · Schur multiplier (H2) = C1

Aliases

direct productC4×C29×C43⋊C7
unambiguous semidirect product(C4×C43)⋊(C7×C29)

Splittings

Fitting, HallC4×C29×C43 ⋊ C7
derived, SylowC43 ⋊ C4×C7×C29
HallC29×C43 ⋊ C4×C7
HallC4×C43 ⋊ C7×C29

Subgroups

subgroupG/H
center, hypercenterC4×C29C43⋊C7
commutator, hypocenterC43C4×C7×C29
FrattiniC2C2×C29×C43⋊C7
FittingC4×C29×C43C7
socleC2×C29×C43C2×C7
prime radicalC2×C29×C43⋊C7C2
cosocleC2×C43C2×C7×C29
LCSG ▷ C43
UCSC1 ◁ C4×C29

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4988

Conjugacy classes & character table

1508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34916, 2);