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C3×ΓL(1,𝔽8)×D67 #22554752

order8442
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×D67

Splittings

Fitting, socleC3×C7×C67 ⋊ C2×C3
derived, HallC7×C67 ⋊ C2×C32
HallC3×ΓL(1,𝔽8)×C67 ⋊ C2
HallC7×D67 ⋊ C32
SylowC67 ⋊ C2×C3×ΓL(1,𝔽8)
SylowC7 ⋊ C32×D67

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×D67
commutator, hypocenterC7×C67C2×C32
FrattiniC1G
Fitting, socleC3×C7×C67C2×C3
LCSG ▷ C7×C67
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

525 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×D67, C3⋊AGL(1,𝔽7)×D67, D3×ΓL(1,𝔽8)×D67, …
maximal normal subgroup ofC3×AGL(1,𝔽7)×D67, C3⋊AGL(1,𝔽7)×D67, D3×ΓL(1,𝔽8)×D67, …
maximal quotient ofC3×ΓL(1,𝔽8)×Dic67, C2×C3×ΓL(1,𝔽8)×D67

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8442, 39);