Finite Group Databasebeta

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Dic3×C13×C29⋊C7 #44539731

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

Aliases

direct productDic3×C13×C29⋊C7
unambiguous semidirect productC3⋊(C4×C13×C29⋊C7)
unambiguous semidirect product(Dic3×C29)⋊(C7×C13)
unambiguous semidirect product(Dic3×C13×C29)⋊C7

Splittings

derived, HallC3×C29 ⋊ C4×C7×C13
HallC3×C13×C29⋊C7 ⋊ C4
HallDic3×C13×C29 ⋊ C7
HallC3×C13×C29 ⋊ C4×C7
HallC3×C29⋊C7 ⋊ C4×C13
HallC13×C29 ⋊ C7×Dic3
HallDic3×C29 ⋊ C7×C13
HallC3×C13 ⋊ C4×C29⋊C7
SylowC29 ⋊ C7×Dic3×C13
SylowC3 ⋊ C4×C13×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C13D3×C29⋊C7
commutator, hypocenterC3×C29C4×C7×C13
FrattiniC2D3×C13×C29⋊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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 26);