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C4×C79×C13⋊C9 #49149356

order36972
automorphism?
homologyAbelianization (H1) = C4×C9×C79 · Schur multiplier (H2) = C1

Aliases

direct productC4×C79×C13⋊C9
unambiguous semidirect product(C4×C13)⋊(C9×C79)

Splittings

derived, SylowC13 ⋊ C4×C9×C79
HallC4×C13×C79 ⋊ C9
HallC13×C79 ⋊ C4×C9
HallC4×C13 ⋊ C9×C79

Subgroups

subgroupG/H
center, hypercenterC3×C4×C79C13⋊C3
commutator, hypocenterC13C4×C9×C79
FrattiniC2×C3C2×C13⋊C3×C79
FittingC3×C4×C13×C79C3
socle, prime radicalC2×C3×C13×C79C2×C3
cosocleC2×C3×C13C2×C3×C79
LCSG ▷ C13
UCSC1 ◁ C3×C4×C79

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36972

Conjugacy classes & character table

6636 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 4);