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C11×C3⋊(C17⋊AGL(1,𝔽7)) #37555640

order23562
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(C17⋊AGL(1,𝔽7))
unambiguous semidirect productC3⋊(C11×C17⋊AGL(1,𝔽7))
unambiguous semidirect productC17⋊(C11×C3⋊AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×D51)
unambiguous semidirect productD357⋊(C3×C11)
unambiguous semidirect product(C11×D357)⋊C3

Splittings

Fitting, socleC3×C7×C11×C17 ⋊ C2×C3
derivedC3×C7×C17 ⋊ C2×C3×C11
HallC3×C11×C17×ΓL(1,𝔽8) ⋊ C2
HallC7×C11×C17 ⋊ C3×D3
HallC3×C17×ΓL(1,𝔽8) ⋊ C2×C11
HallC3×C11×ΓL(1,𝔽8) ⋊ D17
HallC11×C17 ⋊ C3⋊AGL(1,𝔽7)
HallC7×C17 ⋊ C3×D3×C11
HallC7×C11 ⋊ C3×D51
HallC3×ΓL(1,𝔽8) ⋊ C11×D17
SylowC17 ⋊ C11×C3⋊AGL(1,𝔽7)
SylowC7 ⋊ C3×C11×D51

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C17⋊AGL(1,𝔽7))
commutator, cosocle, hypocenterC3×C7×C17C2×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C17C2×C3
LCSG ▷ C3×C7×C17
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 34);