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C9×C13×Dic47 #36347162

order21996
automorphism?
homologyAbelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC9×C13×Dic47
unambiguous semidirect productC47⋊(C4×C9×C13)

Splittings

derived, SylowC47 ⋊ C4×C9×C13
HallC9×C13×C47 ⋊ C4
HallC13×C47 ⋊ C4×C9
HallC9×C47 ⋊ C4×C13

Subgroups

subgroupG/H
center, hypercenterC2×C9×C13D47
commutator, hypocenterC47C4×C9×C13
FrattiniC2×C3C3×C13×D47
FittingC2×C9×C13×C47C2
socle, prime radicalC2×C3×C13×C47C2×C3
cosocleC2×C3×C47C2×C3×C13
LCSG ▷ C47
UCSC1 ◁ C2×C9×C13

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21996

Conjugacy classes & character table

5850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 3);