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C3×#261×C121 #34038338

order18876
automorphism?
homologyAbelianization (H1) = C3×C4×C121 · Schur multiplier (H2) = C1

Aliases

direct productC3×#261×C121

Splittings

Fitting, HallC3×C13×C121 ⋊ C4
derived, SylowC13 ⋊ C3×C4×C121
HallC13×C121 ⋊ C3×C4
HallC3×C13 ⋊ C4×C121

Subgroups

subgroupG/H
center, hypercenterC3×C121#261
commutator, hypocenterC13C3×C4×C121
FrattiniC11C3×C11×#261
FittingC3×C13×C121C4
socleC3×C11×C13C4×C11
prime radicalC3×C11×D13C2×C11
cosocleC11×D13C2×C3×C11
LCSG ▷ C13
UCSC1 ◁ C3×C121

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4719

Conjugacy classes & character table

2541 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18876, 20);