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C23×ΓL(1,𝔽8)⋊#595 #45659262

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

Aliases

direct productC23×ΓL(1,𝔽8)⋊#595
unambiguous semidirect productΓL(1,𝔽8)⋊(C23×#595)
unambiguous semidirect product(C7⋊#595)⋊(C3×C23)
unambiguous semidirect product(C23×C7⋊#595)⋊C3

Splittings

Fitting, socle, HallC7×C17×C23 ⋊ C3×C4
derived, HallC7×C17 ⋊ C3×C4×C23
HallC23×C7⋊#595 ⋊ C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C4
HallΓL(1,𝔽8)×C23 ⋊ #595
HallC7⋊#595 ⋊ C3×C23
HallC17×C23 ⋊ ΓL(1,𝔽8)⋊C4
HallC17×ΓL(1,𝔽8) ⋊ C4×C23
HallC7×C23 ⋊ C3×#595
HallΓL(1,𝔽8) ⋊ C23×#595
SylowC17 ⋊ C23×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C23×#595

Subgroups

subgroupG/H
center, hypercenterC23ΓL(1,𝔽8)⋊#595
commutator, hypocenterC7×C17C3×C4×C23
FrattiniC1G
Fitting, socleC7×C17×C23C3×C4
prime radicalΓL(1,𝔽8)×C23×D17C2
cosocleC7×D17C2×C3×C23
LCSG ▷ C7×C17
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2737

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 27);