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C2×C3×D1955 #37553357

order23460
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D1955
unambiguous semidirect product(C2×C5)⋊(C3×D391)
unambiguous semidirect product(C2×C17)⋊(C3×D115)
unambiguous semidirect product(C2×C23)⋊(C3×D85)

Splittings

Fitting, socleC2×C3×C5×C17×C23 ⋊ C2
derived, HallC5×C17×C23 ⋊ C22×C3
HallC3×C5×C17×C23 ⋊ C22
HallC3×C17×C23 ⋊ C2×D5
HallC17×C23 ⋊ C2×C3×D5
HallC3×C5×C23 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D23
HallC5×C23 ⋊ C2×C3×D17
HallC5×C17 ⋊ C2×C3×D23
HallC3×C23 ⋊ C2×D85
HallC3×C17 ⋊ C2×D115
SylowC23 ⋊ C2×C3×D85
SylowC17 ⋊ C2×C3×D115
HallC3×C5 ⋊ C2×D391
SylowC5 ⋊ C2×C3×D391

Subgroups

subgroupG/H
center, hypercenterC2×C3D1955
commutator, cosocle, hypocenterC5×C17×C23C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C23C2
LCSG ▷ C5×C17×C23
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11730

Conjugacy classes & character table

5874 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 84);