Finite Group Databasebeta

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C3×Dic3×C71⋊C7 #31822031

order17892
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C71⋊C7
unambiguous semidirect productC3⋊(C3×C4×C71⋊C7)
unambiguous semidirect product(Dic3×C71)⋊(C3×C7)
unambiguous semidirect product(C3×Dic3×C71)⋊C7

Splittings

derivedC3×C71 ⋊ C3×C4×C7
HallC32×C71⋊C7 ⋊ C4
HallC3×Dic3×C71 ⋊ C7
HallC32×C71 ⋊ C4×C7
SylowC71 ⋊ C3×C7×Dic3
SylowC32 ⋊ C4×C71⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×C71⋊C7
commutator, hypocenterC3×C71C3×C4×C7
FrattiniC2C3×D3×C71⋊C7
Fitting, socleC2×C32×C71C2×C7
prime radicalC2×C32×C71⋊C7C2
cosocleC2×C3×C71C2×C3×C7
LCSG ▷ C3×C71
UCSC1 ◁ C2×C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 852

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17892, 48);