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C7×C3⋊#10625193 #29509682

order15540
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊#10625193
unambiguous semidirect productC3⋊(C7×#10625193)

Splittings

Fitting, socle, HallC3×C5×C7×C37 ⋊ C4
derived, HallC3×C5×C37 ⋊ C4×C7
HallC5×C7×C37 ⋊ Dic3
HallC3×C7×C37 ⋊ AGL(1,𝔽5)
HallC7×C37 ⋊ ΓL(1,𝔽16)
HallC5×C37 ⋊ C7×Dic3
HallC3×C37 ⋊ C7×AGL(1,𝔽5)
HallC3×C5×C7 ⋊ Dic37
SylowC37 ⋊ C7×ΓL(1,𝔽16)
HallC5×C7 ⋊ Dic111
HallC3×C7 ⋊ #10625193
HallC3×C5 ⋊ C7×Dic37
SylowC5 ⋊ C7×Dic111
SylowC3 ⋊ C7×#10625193

Subgroups

subgroupG/H
center, hypercenterC7C3⋊#10625193
commutator, hypocenterC3×C5×C37C4×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C37C4
prime radicalC3×C7×D5×C37C2
cosocleC3×D5×C37C2×C7
LCSG ▷ C3×C5×C37
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3885

Conjugacy classes & character table

1575 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15540, 184);