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C13×C3⋊(Dic29⋊C7) #44539732

order31668
automorphism?
homologyAbelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊(Dic29⋊C7)
unambiguous semidirect productC3⋊(C13×Dic29⋊C7)
unambiguous semidirect productDic87⋊(C7×C13)
unambiguous semidirect product(C13×Dic87)⋊C7

Splittings

derived, HallC3×C29 ⋊ C4×C7×C13
HallC3×C13×C29⋊C7 ⋊ C4
HallC13×Dic87 ⋊ C7
HallC13×C29⋊C7 ⋊ Dic3
HallC3×C13×C29 ⋊ C4×C7
HallC3×C29⋊C7 ⋊ C4×C13
HallC13×C29 ⋊ C7×Dic3
HallDic87 ⋊ C7×C13
HallC29⋊C7 ⋊ Dic3×C13
HallC3×C13 ⋊ Dic29⋊C7
SylowC29 ⋊ C7×Dic3×C13
SylowC3 ⋊ C13×Dic29⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊(D29⋊C7)
commutator, hypocenterC3×C29C4×C7×C13
FrattiniC2C13×C3⋊(D29⋊C7)
Fitting, socleC2×C3×C13×C29C2×C7
prime radicalC2×C3×C13×C29⋊C7C2
cosocleC2×C3×C29C2×C7×C13
LCSG ▷ C3×C29
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4524

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 27);