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C3×ΓL(1,𝔽8)×Dic43 #24925512

order10836
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×Dic43

Splittings

derived, HallC7×C43 ⋊ C32×C4
HallC3×ΓL(1,𝔽8)×C43 ⋊ C4
HallC7×Dic43 ⋊ C32
SylowC43 ⋊ C3×C4×ΓL(1,𝔽8)
SylowC7 ⋊ C32×Dic43

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×D43
commutator, hypocenterC7×C43C32×C4
FrattiniC2C3×ΓL(1,𝔽8)×D43
Fitting, socleC2×C3×C7×C43C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C43C2
cosocleC2×C7×C43C2×C32
LCSG ▷ C7×C43
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

690 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 104);