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C2×D39×C121 #34038356

order18876
automorphism?
homologyAbelianization (H1) = C22×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×D39×C121
unambiguous semidirect product(C2×C3)⋊(D13×C121)
unambiguous semidirect product(C2×C13)⋊(D3×C121)

Splittings

FittingC2×C3×C13×C121 ⋊ C2
derived, HallC3×C13 ⋊ C22×C121
HallC3×C13×C121 ⋊ C22
HallC13×C121 ⋊ C2×D3
HallC3×C121 ⋊ C2×D13
SylowC13 ⋊ C2×D3×C121
SylowC3 ⋊ C2×D13×C121

Subgroups

subgroupG/H
center, hypercenterC2×C121D39
commutator, hypocenterC3×C13C22×C121
FrattiniC11C2×C11×D39
FittingC2×C3×C13×C121C2
socleC2×C3×C11×C13C2×C11
prime radicalC2×C11×D39C11
cosocleC3×C11×C13C22×C11
LCSG ▷ C3×C13
UCSC1 ◁ C2×C121

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9438

Conjugacy classes & character table

5082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18876, 38);