Finite Group Databasebeta

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C2×C37⋊C3×C121 #41001728

order26862
automorphism?
homologyAbelianization (H1) = C2×C3×C121 · Schur multiplier (H2) = C1

Aliases

direct productC2×C37⋊C3×C121
unambiguous semidirect product(C2×C37)⋊(C3×C121)
unambiguous semidirect product(C2×C37×C121)⋊C3

Splittings

Fitting, HallC2×C37×C121 ⋊ C3
derived, SylowC37 ⋊ C2×C3×C121
HallC37×C121 ⋊ C2×C3
HallC2×C37 ⋊ C3×C121

Subgroups

subgroupG/H
center, hypercenterC2×C121C37⋊C3
commutator, hypocenterC37C2×C3×C121
FrattiniC11C2×C11×C37⋊C3
FittingC2×C37×C121C3
socleC2×C11×C37C3×C11
prime radicalC2×C11×C37⋊C3C11
cosocleC11×C37C2×C3×C11
LCSG ▷ C37
UCSC1 ◁ C2×C121

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8954

Conjugacy classes & character table

3630 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26862, 2);