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C4×C29×C29⋊C7 #37555395

order23548
automorphism?
homologyAbelianization (H1) = C4×C7×C29 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC4×C292 ⋊ C7
derivedC29 ⋊ C4×C7×C29
SylowC292 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC4×C29C29⋊C7
commutator, hypocenterC29C4×C7×C29
FrattiniC2C2×C29×C29⋊C7
FittingC4×C292C7
socleC2×C292C2×C7
prime radicalC2×C29×C29⋊C7C2
cosocleC2×C29C2×C7×C29
LCSG ▷ C29
UCSC1 ◁ C4×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 812

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23548, 32);