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ΓL(1,𝔽8)×C43×Dic11 #51432297

order39732
automorphism?
homologyAbelianization (H1) = C3×C4×C43 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C43×Dic11

Splittings

derived, HallC7×C11 ⋊ C3×C4×C43
HallC7×C43×Dic11 ⋊ C3
HallC11×ΓL(1,𝔽8)×C43 ⋊ C4
HallC7×C11×C43 ⋊ C3×C4
HallC11×C43 ⋊ C4×ΓL(1,𝔽8)
HallC7×Dic11 ⋊ C3×C43
HallC7×C43 ⋊ C3×Dic11
HallC11×ΓL(1,𝔽8) ⋊ C4×C43
SylowC11 ⋊ C4×ΓL(1,𝔽8)×C43
SylowC7 ⋊ C3×C43×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C43ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C3×C4×C43
FrattiniC2ΓL(1,𝔽8)×D11×C43
Fitting, socleC2×C7×C11×C43C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C2×C43

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(39732, 35);