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D29×(C31⋊C3)⋊C5 #41004216

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

Aliases

direct productD29×(C31⋊C3)⋊C5
unambiguous semidirect productC29⋊(C2×(C31⋊C3)⋊C5)
unambiguous semidirect product(D29×C31⋊C3)⋊C5
unambiguous semidirect product(D29×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socle, derived, HallC29×C31 ⋊ C2×C3×C5
HallC29×(C31⋊C3)⋊C5 ⋊ C2
HallD29×ΓL(1,𝔽32) ⋊ C3
HallD29×C31⋊C3 ⋊ C5
HallC29×ΓL(1,𝔽32) ⋊ C2×C3
HallC29×C31⋊C3 ⋊ C2×C5
HallC31×D29 ⋊ C3×C5
HallΓL(1,𝔽32) ⋊ C3×D29
HallC31⋊C3 ⋊ C5×D29
SylowC31 ⋊ C3×C5×D29
SylowC29 ⋊ C2×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC29×C31C2×C3×C5
LCSG ▷ C29×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 899

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 35);