Finite Group Databasebeta

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C3×C13×(C67⋊C3)⋊C4 #44535646

order31356
automorphism?
homologyAbelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC3×C13×(C67⋊C3)⋊C4
unambiguous semidirect product(C67⋊C3)⋊(C3×C4×C13)
unambiguous semidirect productDic67⋊(C32×C13)
unambiguous semidirect product(C3×Dic67)⋊(C3×C13)

Splittings

derived, SylowC67 ⋊ C32×C4×C13
HallC3×C13×C67⋊C3 ⋊ C4
HallC13×Dic67 ⋊ C32
HallC13×C67 ⋊ C32×C4
HallC3×C67⋊C3 ⋊ C4×C13
HallDic67 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D67⋊C3
commutator, hypocenterC67C32×C4×C13
FrattiniC2C3×C13×D67⋊C3
Fitting, socleC2×C3×C13×C67C2×C3
prime radicalC2×C3×C13×C67⋊C3C2
cosocleC2×C67C2×C32×C13
LCSG ▷ C67
UCSC1 ◁ C2×C3×C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10452

Conjugacy classes & character table

1326 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 82);