Finite Group Databasebeta

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C2×C29×D11⋊C25 #44541982

order31900
automorphism?
homologyAbelianization (H1) = C22×C25×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C29×D11⋊C25
unambiguous semidirect productD11⋊(C2×C25×C29)
unambiguous semidirect product(C2×D11)⋊(C25×C29)
unambiguous semidirect product(C11⋊C25)⋊(C22×C29)
unambiguous semidirect product(C2×C11⋊C25)⋊(C2×C29)
unambiguous semidirect product(C2×D11×C29)⋊C25

Splittings

derived, SylowC11 ⋊ C22×C25×C29
HallC29×C11⋊C25 ⋊ C22
HallC2×D11×C29 ⋊ C25
HallC11×C29 ⋊ C22×C25
HallC11⋊C25 ⋊ C22×C29
HallC2×D11 ⋊ C25×C29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C29AGL(1,𝔽11)
commutator, hypocenterC11C22×C25×C29
FrattiniC5C2×C29×AGL(1,𝔽11)
Fitting, socleC2×C5×C11×C29C2×C5
prime radicalC2×C5×D11×C29C5
cosocleC5×C11C22×C5×C29
LCSG ▷ C11
UCSC1 ◁ C2×C5×C29

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15950

Conjugacy classes & character table

3190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31900, 17);