Finite Group Databasebeta

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Dic3×C17×C43⋊C3 #39911645

order26316
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C17×C43⋊C3
unambiguous semidirect productC3⋊(C4×C17×C43⋊C3)
unambiguous semidirect product(Dic3×C43)⋊(C3×C17)
unambiguous semidirect product(Dic3×C17×C43)⋊C3

Splittings

derivedC3×C43 ⋊ C3×C4×C17
HallC3×C17×C43⋊C3 ⋊ C4
HallC17×C43 ⋊ C3×Dic3
HallC3×C43⋊C3 ⋊ C4×C17
SylowC43 ⋊ C3×Dic3×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D3×C43⋊C3
commutator, hypocenterC3×C43C3×C4×C17
FrattiniC2D3×C17×C43⋊C3
Fitting, socleC2×C3×C17×C43C2×C3
prime radicalC2×C3×C17×C43⋊C3C2
cosocleC2×C3×C43C2×C3×C17
LCSG ▷ C3×C43
UCSC1 ◁ C2×C17

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8772

Conjugacy classes & character table

1734 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26316, 46);