Finite Group Databasebeta

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C3×(C43⋊C3)⋊Dic17 #39911642

order26316
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C43⋊C3)⋊Dic17
unambiguous semidirect product(C43⋊C3)⋊(C3×Dic17)
unambiguous semidirect productDic731⋊C32
unambiguous semidirect product(C3×Dic731)⋊C3

Splittings

derived, HallC17×C43 ⋊ C32×C4
HallC3×C17×C43⋊C3 ⋊ C4
HallDic731 ⋊ C32
HallC3×C43⋊C3 ⋊ Dic17
SylowC43 ⋊ C32×Dic17
SylowC17 ⋊ C3×(C43⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3C17⋊(D43⋊C3)
commutator, hypocenterC17×C43C32×C4
FrattiniC2C3×C17⋊(D43⋊C3)
Fitting, socleC2×C3×C17×C43C2×C3
prime radicalC2×C3×C17×C43⋊C3C2
cosocleC2×C17×C43C2×C32
LCSG ▷ C17×C43
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8772

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26316, 43);