Finite Group Databasebeta

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C2×D41×C121 #34090752

order19844
automorphism?
homologyAbelianization (H1) = C22×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×D41×C121
unambiguous semidirect productC41⋊(C22×C121)
unambiguous semidirect product(C2×C41)⋊(C2×C121)

Splittings

FittingC2×C41×C121 ⋊ C2
derived, SylowC41 ⋊ C22×C121
HallC41×C121 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C121D41
commutator, hypocenterC41C22×C121
FrattiniC11C2×C11×D41
FittingC2×C41×C121C2
socleC2×C11×C41C2×C11
prime radicalC2×C11×D41C11
cosocleC11×C41C22×C11
LCSG ▷ C41
UCSC1 ◁ C2×C121

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9922

Conjugacy classes & character table

5324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19844, 9);