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C2×C5×#14268592 #31825462

order18060
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×#14268592

Splittings

Fitting, socleC2×C5×C7×C43 ⋊ C2×C3
derived, HallC7×C43 ⋊ C22×C3×C5
HallC2×C5×D7×C43 ⋊ C3
HallC5×#11744749 ⋊ C22
HallC5×C7×C43 ⋊ C22×C3
HallC2×D7×C43 ⋊ C3×C5
Hall#11744749 ⋊ C22×C5
HallC5×C43 ⋊ C2×AGL(1,𝔽7)
HallC2×C5×D7 ⋊ C43⋊C3
SylowC43 ⋊ C2×C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C22×C43⋊C3
HallC2×D7 ⋊ C5×C43⋊C3
SylowC7 ⋊ C22×C5×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#14268592
commutator, cosocle, hypocenterC7×C43C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C43C2×C3
LCSG ▷ C7×C43
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3010

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18060, 138);