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C3×C7×ΓL(1,𝔽8)×D19 #30660756

order16758
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×ΓL(1,𝔽8)×D19

Splittings

Fitting, socleC3×C72×C19 ⋊ C2×C3
derivedC7×C19 ⋊ C2×C32×C7
HallC3×C7×C19×ΓL(1,𝔽8) ⋊ C2
HallC72×D19 ⋊ C32
HallC72×C19 ⋊ C2×C32
SylowC72 ⋊ C32×D19
SylowC19 ⋊ C2×C3×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC3×C7ΓL(1,𝔽8)×D19
commutator, cosocle, hypocenterC7×C19C2×C32×C7
FrattiniC1G
Fitting, socleC3×C72×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C3×C7

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1197

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×D19×AGL(1,𝔽7), C3×D19×ΓL(1,𝔽8)⋊D7, C3×D7×ΓL(1,𝔽8)×D19, …
maximal normal subgroup ofC3×C7×D19×AGL(1,𝔽7), C3×D19×ΓL(1,𝔽8)⋊D7, C3×D7×ΓL(1,𝔽8)×D19, …
maximal quotient ofC3×C7×ΓL(1,𝔽8)×Dic19, C2×C3×C7×ΓL(1,𝔽8)×D19

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 283);