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C3×C4×(C79⋊C3)⋊C13 #49149448

order36972
automorphism?
homologyAbelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×(C79⋊C3)⋊C13
unambiguous semidirect product(C4×C79⋊C3)⋊(C3×C13)
unambiguous semidirect product(C3×C4×C79⋊C3)⋊C13
unambiguous semidirect product(C4×C79⋊C13)⋊C32
unambiguous semidirect product(C3×C4×C79⋊C13)⋊C3

Splittings

FittingC3×C4×C79 ⋊ C3×C13
derived, SylowC79 ⋊ C32×C4×C13
HallC4×C79⋊C13 ⋊ C32
HallC3×C4×C79⋊C3 ⋊ C13
HallC79⋊C13 ⋊ C32×C4
HallC3×C79⋊C3 ⋊ C4×C13
HallC4×C79 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC3×C4(C79⋊C3)⋊C13
commutator, hypocenterC79C32×C4×C13
FrattiniC2C2×C3×(C79⋊C3)⋊C13
FittingC3×C4×C79C3×C13
socleC2×C3×C79C2×C3×C13
prime radicalC2×C3×(C79⋊C3)⋊C13C2
cosocleC2×C79C2×C32×C13
LCSG ▷ C79
UCSC1 ◁ C3×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 948

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 96);