Finite Group Databasebeta

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C23×D17×AGL(1,𝔽7) #45659264

order32844
automorphism?
homologyAbelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C2

Aliases

direct productC23×D17×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C23×D17)
unambiguous semidirect product(D7×D17)⋊(C3×C23)
unambiguous semidirect product(ΓL(1,𝔽8)×D17)⋊(C2×C23)
unambiguous semidirect product(C17×AGL(1,𝔽7))⋊(C2×C23)
unambiguous semidirect product(C17⋊AGL(1,𝔽7))⋊(C2×C23)
unambiguous semidirect product(D7×C23×D17)⋊C3

Splittings

Fitting, socle, HallC7×C17×C23 ⋊ C22×C3
derived, HallC7×C17 ⋊ C22×C3×C23
HallD7×C23×D17 ⋊ C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C22
HallΓL(1,𝔽8)×C23 ⋊ C2×D17
HallD7×D17 ⋊ C3×C23
HallC17×C23 ⋊ C2×AGL(1,𝔽7)
HallC17×ΓL(1,𝔽8) ⋊ C22×C23
HallC7×C23 ⋊ C2×C3×D17
HallΓL(1,𝔽8) ⋊ C2×C23×D17
SylowC17 ⋊ C2×C23×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×C23×D17

Subgroups

subgroupG/H
center, hypercenterC23D17×AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C17C22×C3×C23
FrattiniC1G
Fitting, socleC7×C17×C23C22×C3
LCSG ▷ C7×C17
UCSC1 ◁ C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2737

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 29);