Finite Group Databasebeta

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C23×D15⋊D17 #37553346

order23460
automorphism?
homologyAbelianization (H1) = C22×C23 · Schur multiplier (H2) = C2

Aliases

direct productC23×D15⋊D17
unambiguous semidirect productD15⋊(C23×D17)
unambiguous semidirect productD51⋊(D5×C23)
unambiguous semidirect productD85⋊(D3×C23)

Splittings

Fitting, socle, HallC3×C5×C17×C23 ⋊ C22
derived, HallC3×C5×C17 ⋊ C22×C23
HallC5×C17×C23 ⋊ C2×D3
HallC3×C17×C23 ⋊ C2×D5
HallC17×C23 ⋊ D3×D5
HallC3×C5×C23 ⋊ C2×D17
HallC5×C23 ⋊ D3×D17
HallC5×C17 ⋊ C2×D3×C23
HallC3×C23 ⋊ D5×D17
HallC3×C17 ⋊ C2×D5×C23
SylowC17 ⋊ D3×D5×C23
HallC3×C5 ⋊ C2×C23×D17
SylowC5 ⋊ D3×C23×D17
SylowC3 ⋊ D5×C23×D17

Subgroups

subgroupG/H
center, hypercenterC23D15⋊D17
commutator, cosocle, hypocenterC3×C5×C17C22×C23
FrattiniC1G
Fitting, socleC3×C5×C17×C23C22
LCSG ▷ C3×C5×C17
UCSC1 ◁ C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5865

Conjugacy classes & character table

1932 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 73);