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C37×(C61⋊C3)⋊C5 #46799656

order33855
automorphism?
homologyAbelianization (H1) = C3×C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×(C61⋊C3)⋊C5
unambiguous semidirect product(C61⋊C3)⋊(C5×C37)
unambiguous semidirect product(C61⋊C5)⋊(C3×C37)
unambiguous semidirect product(C37×C61⋊C3)⋊C5

Splittings

Fitting, socle, HallC37×C61 ⋊ C3×C5
derived, SylowC61 ⋊ C3×C5×C37
HallC37×C61⋊C5 ⋊ C3
HallC37×C61⋊C3 ⋊ C5
HallC61⋊C5 ⋊ C3×C37
HallC61⋊C3 ⋊ C5×C37

Subgroups

subgroupG/H
center, hypercenterC37(C61⋊C3)⋊C5
commutator, cosocle, hypocenterC61C3×C5×C37
FrattiniC1G
Fitting, socleC37×C61C3×C5
LCSG ▷ C61
UCSC1 ◁ C37

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2257

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33855, 7);