Finite Group Databasebeta

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C2×C3×D17×C43⋊C3 #39911675

order26316
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×D17×C43⋊C3
unambiguous semidirect productC17⋊(C22×C3×C43⋊C3)
unambiguous semidirect product(C2×C17)⋊(C2×C3×C43⋊C3)
unambiguous semidirect product(C2×D17×C43)⋊C32
unambiguous semidirect product(C2×C3×D17×C43)⋊C3

Splittings

Fitting, socleC2×C3×C17×C43 ⋊ C2×C3
derived, HallC17×C43 ⋊ C22×C32
HallC3×C17×C43⋊C3 ⋊ C22
HallC2×D17×C43 ⋊ C32
SylowC43 ⋊ C2×C32×D17
SylowC17 ⋊ C22×C3×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D17×C43⋊C3
commutator, cosocle, hypocenterC17×C43C22×C32
FrattiniC1G
Fitting, socleC2×C3×C17×C43C2×C3
LCSG ▷ C17×C43
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4386

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26316, 76);