Finite Group Databasebeta

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C4×C41×C29⋊C7 #45685604

order33292
automorphism?
homologyAbelianization (H1) = C4×C7×C41 · Schur multiplier (H2) = C1

Aliases

direct productC4×C41×C29⋊C7
unambiguous semidirect product(C4×C29)⋊(C7×C41)
unambiguous semidirect product(C4×C29×C41)⋊C7

Splittings

Fitting, HallC4×C29×C41 ⋊ C7
derived, SylowC29 ⋊ C4×C7×C41
HallC29×C41 ⋊ C4×C7
HallC4×C29 ⋊ C7×C41

Subgroups

subgroupG/H
center, hypercenterC4×C41C29⋊C7
commutator, hypocenterC29C4×C7×C41
FrattiniC2C2×C41×C29⋊C7
FittingC4×C29×C41C7
socleC2×C29×C41C2×C7
prime radicalC2×C41×C29⋊C7C2
cosocleC2×C29C2×C7×C41
LCSG ▷ C29
UCSC1 ◁ C4×C41

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4756

Conjugacy classes & character table

1804 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33292, 2);