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C3×C37×C5⋊AGL(1,𝔽7) #37552077

order23310
automorphism?
homologyAbelianization (H1) = C2×C32×C37 · Schur multiplier (H2) = C3

Aliases

direct productC3×C37×C5⋊AGL(1,𝔽7)
unambiguous semidirect productC5⋊(C3×C37×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×D5×C37)
unambiguous semidirect productD35⋊(C32×C37)
unambiguous semidirect product(C3×D35)⋊(C3×C37)

Splittings

Fitting, socleC3×C5×C7×C37 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C32×C37
HallC3×C5×ΓL(1,𝔽8)×C37 ⋊ C2
HallC37×D35 ⋊ C32
HallC3×ΓL(1,𝔽8)×C37 ⋊ D5
HallC5×C7×C37 ⋊ C2×C32
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C37
HallC7×C37 ⋊ C32×D5
HallC5×C37 ⋊ C3×AGL(1,𝔽7)
HallD35 ⋊ C32×C37
HallC3×ΓL(1,𝔽8) ⋊ D5×C37
SylowC7 ⋊ C32×D5×C37
SylowC5 ⋊ C3×C37×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC3×C37C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C2×C32×C37
FrattiniC1G
Fitting, socleC3×C5×C7×C37C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C3×C37

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3885

Conjugacy classes & character table

1887 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 96);