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C3×C29⋊(D31⋊C5) #41004203

order26970
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C29⋊(D31⋊C5)
unambiguous semidirect productC29⋊(C3×D31⋊C5)
unambiguous semidirect product(C3×D899)⋊C5

Splittings

Fitting, socle, HallC3×C29×C31 ⋊ C2×C5
derived, HallC29×C31 ⋊ C2×C3×C5
HallC3×C29×ΓL(1,𝔽32) ⋊ C2
HallC3×D899 ⋊ C5
HallC29×ΓL(1,𝔽32) ⋊ C2×C3
HallD899 ⋊ C3×C5
HallC3×ΓL(1,𝔽32) ⋊ D29
HallΓL(1,𝔽32) ⋊ C3×D29
HallC3×C31 ⋊ C5×D29
HallC3×C29 ⋊ D31⋊C5
SylowC31 ⋊ C3×C5×D29
SylowC29 ⋊ C3×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C29⋊(D31⋊C5)
commutator, cosocle, hypocenterC29×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C29×C31C2×C5
LCSG ▷ C29×C31
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2697

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 22);