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C4×C47×C13⋊C9 #36347161

order21996
automorphism?
homologyAbelianization (H1) = C4×C9×C47 · Schur multiplier (H2) = C1

Aliases

direct productC4×C47×C13⋊C9
unambiguous semidirect product(C4×C13)⋊(C9×C47)
unambiguous semidirect product(C4×C13×C47)⋊C9

Splittings

derived, SylowC13 ⋊ C4×C9×C47
HallC4×C13×C47 ⋊ C9
HallC13×C47 ⋊ C4×C9
HallC4×C13 ⋊ C9×C47

Subgroups

subgroupG/H
center, hypercenterC3×C4×C47C13⋊C3
commutator, hypocenterC13C4×C9×C47
FrattiniC2×C3C2×C13⋊C3×C47
FittingC3×C4×C13×C47C3
socle, prime radicalC2×C3×C13×C47C2×C3
cosocleC2×C3×C13C2×C3×C47
LCSG ▷ C13
UCSC1 ◁ C3×C4×C47

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21996

Conjugacy classes & character table

3948 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 2);