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C4×C5×#11715912 #29509503

order15540
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×#11715912

Splittings

Fitting, HallC4×C5×C7×C37 ⋊ C3
derived, HallC7×C37 ⋊ C3×C4×C5
HallC5×C7×C37 ⋊ C3×C4
HallC4×C7×C37 ⋊ C3×C5
HallC4×C5×C37 ⋊ ΓL(1,𝔽8)
HallC5×C37 ⋊ C4×ΓL(1,𝔽8)
HallC4×C37 ⋊ C5×ΓL(1,𝔽8)
HallC4×C5×C7 ⋊ C37⋊C3
SylowC37 ⋊ C4×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C4×C37⋊C3
HallC4×C7 ⋊ C5×C37⋊C3
SylowC7 ⋊ C4×C5×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C5#11715912
commutator, hypocenterC7×C37C3×C4×C5
FrattiniC2C2×C5×#11715912
FittingC4×C5×C7×C37C3
socleC2×C5×C7×C37C2×C3
prime radicalC2×C5×#11715912C2
cosocleC2×C7×C37C2×C3×C5
LCSG ▷ C7×C37
UCSC1 ◁ C4×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5180

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15540, 5);