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C4×C13⋊C3×C79⋊C3 #49149458

order36972
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC4×C13⋊C3×C79⋊C3
unambiguous semidirect product(C4×C13×C79⋊C3)⋊C3
unambiguous semidirect product(C4×C13⋊C3×C79)⋊C3
unambiguous semidirect product(C4×#15690493)⋊C3
unambiguous semidirect product(C4×#15690494)⋊C3

Splittings

Fitting, HallC4×C13×C79 ⋊ C32
derived, HallC13×C79 ⋊ C32×C4
HallC4×C79 ⋊ C3×C13⋊C3
SylowC79 ⋊ C3×C4×C13⋊C3
HallC4×C13 ⋊ C3×C79⋊C3
SylowC13 ⋊ C3×C4×C79⋊C3

Subgroups

subgroupG/H
center, hypercenterC4C13⋊C3×C79⋊C3
commutator, hypocenterC13×C79C32×C4
FrattiniC2C2×C13⋊C3×C79⋊C3
FittingC4×C13×C79C32
socle, cosocleC2×C13×C79C2×C32
prime radicalC2×C13⋊C3×C79⋊C3C2
LCSG ▷ C13×C79
UCSC1 ◁ C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4108

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 106);