Finite Group Databasebeta

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C23×D705 #44569868

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

Aliases

direct productC23×D705
unambiguous semidirect productC3⋊(C23×D235)
unambiguous semidirect productC5⋊(C23×D141)

Splittings

Fitting, socle, HallC3×C5×C23×C47 ⋊ C2
derived, HallC3×C5×C47 ⋊ C2×C23
HallC5×C23×C47 ⋊ D3
HallC3×C23×C47 ⋊ D5
HallC23×C47 ⋊ D15
HallC3×C5×C23 ⋊ D47
HallC5×C47 ⋊ D3×C23
HallC3×C47 ⋊ D5×C23
HallC5×C23 ⋊ D141
HallC3×C23 ⋊ D235
SylowC47 ⋊ C23×D15
HallC3×C5 ⋊ C23×D47
SylowC5 ⋊ C23×D141
SylowC3 ⋊ C23×D235

Subgroups

subgroupG/H
center, hypercenterC23D705
commutator, cosocle, hypocenterC3×C5×C47C2×C23
FrattiniC1G
Fitting, socleC3×C5×C23×C47C2
LCSG ▷ C3×C5×C47
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16215

Conjugacy classes & character table

8142 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32430, 15);