Finite Group Databasebeta

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C2×C17×D345 #37553363

order23460
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×D345
unambiguous semidirect product(C2×C3)⋊(C17×D115)
unambiguous semidirect product(C2×C5)⋊(C17×D69)
unambiguous semidirect product(C2×C23)⋊(C17×D15)

Splittings

Fitting, socleC2×C3×C5×C17×C23 ⋊ C2
derived, HallC3×C5×C23 ⋊ C22×C17
HallC3×C5×C17×C23 ⋊ C22
HallC5×C17×C23 ⋊ C2×D3
HallC3×C17×C23 ⋊ C2×D5
HallC17×C23 ⋊ C2×D15
HallC3×C5×C17 ⋊ C2×D23
HallC5×C23 ⋊ C2×D3×C17
HallC5×C17 ⋊ C2×D69
HallC3×C23 ⋊ C2×D5×C17
HallC3×C17 ⋊ C2×D115
SylowC23 ⋊ C2×C17×D15
HallC3×C5 ⋊ C2×C17×D23
SylowC5 ⋊ C2×C17×D69
SylowC3 ⋊ C2×C17×D115

Subgroups

subgroupG/H
center, hypercenterC2×C17D345
commutator, cosocle, hypocenterC3×C5×C23C22×C17
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C23C2
LCSG ▷ C3×C5×C23
UCSC1 ◁ C2×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11730

Conjugacy classes & character table

5916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 90);