Finite Group Databasebeta

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C2×ΓL(1,𝔽8)×C23×D17 #45659277

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

Aliases

direct productC2×ΓL(1,𝔽8)×C23×D17
unambiguous semidirect productC17⋊(C22×ΓL(1,𝔽8)×C23)
unambiguous semidirect product(C2×C17)⋊(C2×ΓL(1,𝔽8)×C23)
unambiguous semidirect product(C2×C7×D17)⋊(C3×C23)
unambiguous semidirect product(C2×C7×C23×D17)⋊C3

Splittings

Fitting, socleC2×C7×C17×C23 ⋊ C2×C3
derived, HallC7×C17 ⋊ C22×C3×C23
HallC2×C7×C23×D17 ⋊ C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C22
HallC7×C17×C23 ⋊ C22×C3
HallC2×C7×D17 ⋊ C3×C23
HallC17×C23 ⋊ C22×ΓL(1,𝔽8)
HallC17×ΓL(1,𝔽8) ⋊ C22×C23
HallC7×C23 ⋊ C2×C3×D17
SylowC17 ⋊ C22×ΓL(1,𝔽8)×C23
SylowC7 ⋊ C2×C3×C23×D17

Subgroups

subgroupG/H
center, hypercenterC2×C23ΓL(1,𝔽8)×D17
commutator, cosocle, hypocenterC7×C17C22×C3×C23
FrattiniC1G
Fitting, socleC2×C7×C17×C23C2×C3
LCSG ▷ C7×C17
UCSC1 ◁ C2×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5474

Conjugacy classes & character table

2300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 42);