Finite Group Databasebeta

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C2×C9×C47⋊C23 #34085598

order19458
automorphism?
homologyAbelianization (H1) = C2×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC2×C9×C47⋊C23
unambiguous semidirect product(C2×C47)⋊(C9×C23)
unambiguous semidirect product(C2×C9×C47)⋊C23

Splittings

Fitting, HallC2×C9×C47 ⋊ C23
derived, SylowC47 ⋊ C2×C9×C23
HallC9×C47 ⋊ C2×C23
HallC2×C47 ⋊ C9×C23

Subgroups

subgroupG/H
center, hypercenterC2×C9C47⋊C23
commutator, hypocenterC47C2×C9×C23
FrattiniC3C2×C3×C47⋊C23
FittingC2×C9×C47C23
socleC2×C3×C47C3×C23
prime radicalC2×C3×C47⋊C23C3
cosocleC3×C47C2×C3×C23
LCSG ▷ C47
UCSC1 ◁ C2×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 846

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19458, 2);