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C4×C17×ΓL(1,𝔽8)×C23 #45659237

order32844
automorphism?
homologyAbelianization (H1) = C3×C4×C17×C23 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×ΓL(1,𝔽8)×C23
unambiguous semidirect product(C4×C7)⋊(C3×C17×C23)
unambiguous semidirect product(C4×C7×C17)⋊(C3×C23)
unambiguous semidirect product(C4×C7×C23)⋊(C3×C17)
unambiguous semidirect product(C4×C7×C17×C23)⋊C3

Splittings

Fitting, HallC4×C7×C17×C23 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C17×C23
HallC7×C17×C23 ⋊ C3×C4
HallC4×C7×C23 ⋊ C3×C17
HallC4×C7×C17 ⋊ C3×C23
HallC7×C23 ⋊ C3×C4×C17
HallC7×C17 ⋊ C3×C4×C23
HallC4×C7 ⋊ C3×C17×C23

Subgroups

subgroupG/H
center, hypercenterC4×C17×C23ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C17×C23
FrattiniC2C2×C17×ΓL(1,𝔽8)×C23
FittingC4×C7×C17×C23C3
socleC2×C7×C17×C23C2×C3
prime radicalC2×C17×ΓL(1,𝔽8)×C23C2
cosocleC2×C7C2×C3×C17×C23
LCSG ▷ C7
UCSC1 ◁ C4×C17×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10948

Conjugacy classes & character table

7820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 2);