Finite Group Databasebeta

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C2×C11×D31⋊C25 #46801949

order34100
automorphism?
homologyAbelianization (H1) = C22×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D31⋊C25
unambiguous semidirect productD31⋊(C2×C11×C25)
unambiguous semidirect product(C2×D31)⋊(C11×C25)
unambiguous semidirect product(C31⋊C25)⋊(C22×C11)
unambiguous semidirect product(C2×C31⋊C25)⋊(C2×C11)

Splittings

derived, SylowC31 ⋊ C22×C11×C25
HallC11×C31⋊C25 ⋊ C22
HallC2×C11×D31 ⋊ C25
HallC31⋊C25 ⋊ C22×C11
HallC11×C31 ⋊ C22×C25
HallC2×D31 ⋊ C11×C25

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D31⋊C5
commutator, hypocenterC31C22×C11×C25
FrattiniC5C2×C11×D31⋊C5
Fitting, socleC2×C5×C11×C31C2×C5
prime radicalC2×C5×C11×D31C5
cosocleC5×C31C22×C5×C11
LCSG ▷ C31
UCSC1 ◁ C2×C5×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17050

Conjugacy classes & character table

1430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 40);