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C11×ΓL(1,𝔽8)⋊Dic43 #51432309

order39732
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)⋊Dic43

Splittings

derived, HallC7×C43 ⋊ C3×C4×C11
HallC11×Dic301 ⋊ C3
HallC11×ΓL(1,𝔽8)×C43 ⋊ C4
HallC7×C11×C43 ⋊ C3×C4
HallDic301 ⋊ C3×C11
HallΓL(1,𝔽8)×C43 ⋊ C4×C11
HallC11×C43 ⋊ ΓL(1,𝔽8)⋊C4
HallC11×ΓL(1,𝔽8) ⋊ Dic43
HallC7×C11 ⋊ C3×Dic43
SylowC43 ⋊ C11×ΓL(1,𝔽8)⋊C4
HallΓL(1,𝔽8) ⋊ C11×Dic43
SylowC7 ⋊ C3×C11×Dic43

Subgroups

subgroupG/H
center, hypercenterC2×C11ΓL(1,𝔽8)⋊D43
commutator, hypocenterC7×C43C3×C4×C11
FrattiniC2C11×ΓL(1,𝔽8)⋊D43
Fitting, socleC2×C7×C11×C43C2×C3
LCSG ▷ C7×C43
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2464 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(39732, 47);