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C79×C3⋊(Dic13⋊C3) #49149473

order36972
automorphism?
homologyAbelianization (H1) = C3×C4×C79 · Schur multiplier (H2) = C1

Aliases

direct productC79×C3⋊(Dic13⋊C3)
unambiguous semidirect productC3⋊(C79×Dic13⋊C3)
unambiguous semidirect productDic39⋊(C3×C79)

Splittings

derivedC3×C13 ⋊ C3×C4×C79
HallC3×C13⋊C3×C79 ⋊ C4
HallC13×C79 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C79
SylowC13 ⋊ C3×Dic3×C79

Subgroups

subgroupG/H
center, hypercenterC2×C79C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C3×C4×C79
FrattiniC2C79×C3⋊(D13⋊C3)
Fitting, socleC2×C3×C13×C79C2×C3
prime radicalC2×C3×C13⋊C3×C79C2
cosocleC2×C3×C13C2×C3×C79
LCSG ▷ C3×C13
UCSC1 ◁ C2×C79

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12324

Conjugacy classes & character table

2370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 121);