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C3×C17×C241⋊C3 #49146151

order36873
automorphism?
homologyAbelianization (H1) = C32×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×C17×C241⋊C3
unambiguous semidirect productC241⋊(C32×C17)
unambiguous semidirect product(C3×C241)⋊(C3×C17)
unambiguous semidirect product(C17×C241)⋊C32
unambiguous semidirect product(C3×C17×C241)⋊C3

Splittings

Fitting, socleC3×C17×C241 ⋊ C3
derived, SylowC241 ⋊ C32×C17
HallC17×C241 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C17C241⋊C3
commutator, cosocle, hypocenterC241C32×C17
FrattiniC1G
Fitting, socleC3×C17×C241C3
LCSG ▷ C241
UCSC1 ◁ C3×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12291

Conjugacy classes & character table

4233 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36873, 4);