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C3×C7×ΓL(1,𝔽8)×D13 #26039586

order11466
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×ΓL(1,𝔽8)×D13

Splittings

Fitting, socleC3×C72×C13 ⋊ C2×C3
derivedC7×C13 ⋊ C2×C32×C7
HallC3×C7×C13×ΓL(1,𝔽8) ⋊ C2
HallC72×D13 ⋊ C32
HallC72×C13 ⋊ C2×C32
SylowC72 ⋊ C32×D13
SylowC13 ⋊ C2×C3×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC3×C7ΓL(1,𝔽8)×D13
commutator, cosocle, hypocenterC7×C13C2×C32×C7
FrattiniC1G
Fitting, socleC3×C72×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C3×C7

112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

840 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C7×ΓL(1,𝔽8)×#261, C3×C7×ΓL(1,𝔽8)⋊#261, C3×C7×D13×AGL(1,𝔽7), …
maximal normal subgroup ofC3×C7×ΓL(1,𝔽8)×#261, C3×C7×ΓL(1,𝔽8)⋊#261, C3×C7×D13×AGL(1,𝔽7), …
maximal quotient ofC3×C7×ΓL(1,𝔽8)×Dic13, C2×C3×C7×ΓL(1,𝔽8)×D13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 229);