Finite Group Databasebeta

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C17×AGL(1,𝔽7)×D23 #45659261

order32844
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×AGL(1,𝔽7)×D23
unambiguous semidirect productD7⋊(C3×C17×D23)
unambiguous semidirect product(D7×D23)⋊(C3×C17)
unambiguous semidirect product(ΓL(1,𝔽8)×D23)⋊(C2×C17)
unambiguous semidirect product(C23×AGL(1,𝔽7))⋊(C2×C17)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D23)⋊(C2×C17)
unambiguous semidirect product(D7×C17×D23)⋊C3

Splittings

Fitting, socle, HallC7×C17×C23 ⋊ C22×C3
derived, HallC7×C23 ⋊ C22×C3×C17
HallD7×C17×D23 ⋊ C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C22
HallD7×D23 ⋊ C3×C17
HallΓL(1,𝔽8)×C23 ⋊ C22×C17
HallC17×C23 ⋊ C2×AGL(1,𝔽7)
HallC17×ΓL(1,𝔽8) ⋊ C2×D23
HallC7×C17 ⋊ C2×C3×D23
SylowC23 ⋊ C2×C17×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×C17×D23
SylowC7 ⋊ C2×C3×C17×D23

Subgroups

subgroupG/H
center, hypercenterC17AGL(1,𝔽7)×D23
commutator, cosocle, hypocenterC7×C23C22×C3×C17
FrattiniC1G
Fitting, socleC7×C17×C23C22×C3
LCSG ▷ C7×C23
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2737

Conjugacy classes & character table

1547 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 26);