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C7×C19×C3⋊ΓL(1,𝔽16) #37561594

order23940
automorphism?
homologyAbelianization (H1) = C4×C7×C19 · Schur multiplier (H2) = C3

Aliases

direct productC7×C19×C3⋊ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C7×C19×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C4
derived, HallC32×C5 ⋊ C4×C7×C19
HallC32×C7×C19 ⋊ AGL(1,𝔽5)
HallC32×C5×C19 ⋊ C4×C7
HallC5×C7×C19 ⋊ C3⋊Dic3
HallC32×C5×C7 ⋊ C4×C19
HallC32×C19 ⋊ C7×AGL(1,𝔽5)
HallC5×C19 ⋊ C7×C3⋊Dic3
HallC32×C7 ⋊ C19×AGL(1,𝔽5)
HallC5×C7 ⋊ C19×C3⋊Dic3
SylowC32 ⋊ C7×C19×AGL(1,𝔽5)
SylowC5 ⋊ C7×C19×C3⋊Dic3

Subgroups

subgroupG/H
center, hypercenterC7×C19C3⋊ΓL(1,𝔽16)
commutator, hypocenterC32×C5C4×C7×C19
FrattiniC1G
Fitting, socleC32×C5×C7×C19C4
prime radicalC32×C7×D5×C19C2
cosocleC32×D5C2×C7×C19
LCSG ▷ C32×C5
UCSC1 ◁ C7×C19

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5985

Conjugacy classes & character table

2793 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 726);