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C4×C5×#11744749 #31825329

order18060
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×#11744749

Splittings

Fitting, HallC4×C5×C7×C43 ⋊ C3
derived, HallC7×C43 ⋊ C3×C4×C5
HallC5×C7×C43 ⋊ C3×C4
HallC4×C7×C43 ⋊ C3×C5
HallC4×C5×C43 ⋊ ΓL(1,𝔽8)
HallC5×C43 ⋊ C4×ΓL(1,𝔽8)
HallC4×C43 ⋊ C5×ΓL(1,𝔽8)
HallC4×C5×C7 ⋊ C43⋊C3
SylowC43 ⋊ C4×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C4×C43⋊C3
HallC4×C7 ⋊ C5×C43⋊C3
SylowC7 ⋊ C4×C5×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C5#11744749
commutator, hypocenterC7×C43C3×C4×C5
FrattiniC2C2×C5×#11744749
FittingC4×C5×C7×C43C3
socleC2×C5×C7×C43C2×C3
prime radicalC2×C5×#11744749C2
cosocleC2×C7×C43C2×C3×C5
LCSG ▷ C7×C43
UCSC1 ◁ C4×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6020

Conjugacy classes & character table

2060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18060, 5);