Finite Group Databasebeta

← Prev (#45659272) Next (#45659274) →

C2×C17×ΓL(1,𝔽8)⋊D23 #45659273

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

Aliases

direct productC2×C17×ΓL(1,𝔽8)⋊D23
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C17×D23)
unambiguous semidirect product(C2×C23)⋊(C17×AGL(1,𝔽7))
unambiguous semidirect product(C2×D161)⋊(C3×C17)
unambiguous semidirect product(C2×C17×D161)⋊C3

Splittings

Fitting, socleC2×C7×C17×C23 ⋊ C2×C3
derived, HallC7×C23 ⋊ C22×C3×C17
HallC2×C17×D161 ⋊ C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C22
HallC7×C17×C23 ⋊ C22×C3
HallC2×D161 ⋊ 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, hypercenterC2×C17ΓL(1,𝔽8)⋊D23
commutator, cosocle, hypocenterC7×C23C22×C3×C17
FrattiniC1G
Fitting, socleC2×C7×C17×C23C2×C3
LCSG ▷ C7×C23
UCSC1 ◁ C2×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5474

Conjugacy classes & character table

2108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 38);