Finite Group Databasebeta

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C2×C3×C5×C47⋊C23 #44569855

order32430
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C5×C47⋊C23
unambiguous semidirect product(C2×C47)⋊(C3×C5×C23)
unambiguous semidirect product(C2×C3×C47)⋊(C5×C23)
unambiguous semidirect product(C2×C5×C47)⋊(C3×C23)
unambiguous semidirect product(C2×C3×C5×C47)⋊C23

Splittings

Fitting, socle, HallC2×C3×C5×C47 ⋊ C23
derived, SylowC47 ⋊ C2×C3×C5×C23
HallC3×C5×C47 ⋊ C2×C23
HallC2×C5×C47 ⋊ C3×C23
HallC2×C3×C47 ⋊ C5×C23
HallC5×C47 ⋊ C2×C3×C23
HallC3×C47 ⋊ C2×C5×C23
HallC2×C47 ⋊ C3×C5×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C47⋊C23
commutator, cosocle, hypocenterC47C2×C3×C5×C23
FrattiniC1G
Fitting, socleC2×C3×C5×C47C23
LCSG ▷ C47
UCSC1 ◁ C2×C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1410

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32430, 2);