Finite Group Databasebeta

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C11×C17×Dic13⋊C3 #44415727

order29172
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C11×C17)
unambiguous semidirect product(C11×Dic13)⋊(C3×C17)
unambiguous semidirect product(C17×Dic13)⋊(C3×C11)
unambiguous semidirect product(C11×C17×Dic13)⋊C3

Splittings

derived, SylowC13 ⋊ C3×C4×C11×C17
HallC11×C17×Dic13 ⋊ C3
HallC11×C17×C13⋊C3 ⋊ C4
HallC11×C13×C17 ⋊ C3×C4
HallC17×Dic13 ⋊ C3×C11
HallC17×C13⋊C3 ⋊ C4×C11
HallC11×Dic13 ⋊ C3×C17
HallC11×C13⋊C3 ⋊ C4×C17
HallC13×C17 ⋊ C3×C4×C11
HallC11×C13 ⋊ C3×C4×C17
HallDic13 ⋊ C3×C11×C17
HallC13⋊C3 ⋊ C4×C11×C17

Subgroups

subgroupG/H
center, hypercenterC2×C11×C17D13⋊C3
commutator, hypocenterC13C3×C4×C11×C17
FrattiniC2C11×C17×D13⋊C3
Fitting, socleC2×C11×C13×C17C2×C3
prime radicalC2×C11×C17×C13⋊C3C2
cosocleC2×C13C2×C3×C11×C17
LCSG ▷ C13
UCSC1 ◁ C2×C11×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9724

Conjugacy classes & character table

2992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 19);