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C11×ΓL(1,𝔽8)⋊#595 #30628105

order15708
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)⋊#595
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×#595)
unambiguous semidirect product(C7⋊#595)⋊(C3×C11)
unambiguous semidirect product(C11×C7⋊#595)⋊C3

Splittings

Fitting, socle, HallC7×C11×C17 ⋊ C3×C4
derived, HallC7×C17 ⋊ C3×C4×C11
HallC11×C7⋊#595 ⋊ C3
HallC11×C17×ΓL(1,𝔽8) ⋊ C4
HallC7⋊#595 ⋊ C3×C11
HallC17×ΓL(1,𝔽8) ⋊ C4×C11
HallC11×ΓL(1,𝔽8) ⋊ #595
HallC11×C17 ⋊ ΓL(1,𝔽8)⋊C4
HallC7×C11 ⋊ C3×#595
HallΓL(1,𝔽8) ⋊ C11×#595
SylowC17 ⋊ C11×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C11×#595

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)⋊#595
commutator, hypocenterC7×C17C3×C4×C11
FrattiniC1G
Fitting, socleC7×C11×C17C3×C4
prime radicalC11×ΓL(1,𝔽8)×D17C2
cosocleC7×D17C2×C3×C11
LCSG ▷ C7×C17
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1309

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 26);