Finite Group Databasebeta

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C2×C17×ΓL(1,𝔽8)×D23 #45659276

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

Aliases

direct productC2×C17×ΓL(1,𝔽8)×D23
unambiguous semidirect productC23⋊(C22×C17×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C23)⋊(C2×C17×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×D23)⋊(C3×C17)
unambiguous semidirect product(C2×C7×C17×D23)⋊C3

Splittings

Fitting, socleC2×C7×C17×C23 ⋊ C2×C3
derived, HallC7×C23 ⋊ C22×C3×C17
HallC2×C7×C17×D23 ⋊ C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C22
HallC7×C17×C23 ⋊ C22×C3
HallC2×C7×D23 ⋊ C3×C17
HallΓL(1,𝔽8)×C23 ⋊ C22×C17
HallC17×C23 ⋊ C22×ΓL(1,𝔽8)
HallC7×C17 ⋊ C2×C3×D23
SylowC23 ⋊ C22×C17×ΓL(1,𝔽8)
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

2210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 41);