Finite Group Databasebeta

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C17×(C67⋊C3)⋊C11 #49178028

order37587
automorphism?
homologyAbelianization (H1) = C3×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×(C67⋊C3)⋊C11
unambiguous semidirect product(C67⋊C3)⋊(C11×C17)
unambiguous semidirect product(C67⋊C11)⋊(C3×C17)
unambiguous semidirect product(C17×C67⋊C3)⋊C11
unambiguous semidirect product(C17×C67⋊C11)⋊C3

Splittings

Fitting, socle, HallC17×C67 ⋊ C3×C11
derived, SylowC67 ⋊ C3×C11×C17
HallC17×C67⋊C11 ⋊ C3
HallC17×C67⋊C3 ⋊ C11
HallC67⋊C11 ⋊ C3×C17
HallC67⋊C3 ⋊ C11×C17

Subgroups

subgroupG/H
center, hypercenterC17(C67⋊C3)⋊C11
commutator, cosocle, hypocenterC67C3×C11×C17
FrattiniC1G
Fitting, socleC17×C67C3×C11
LCSG ▷ C67
UCSC1 ◁ C17

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1139

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37587, 4);