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C13×ΓL(1,𝔽8)×D19 #23780543

order10374
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)×D19

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C13
HallC13×C19×ΓL(1,𝔽8) ⋊ C2
HallC7×C13×D19 ⋊ C3
HallC19×ΓL(1,𝔽8) ⋊ C2×C13
HallC7×D19 ⋊ C3×C13
HallC13×C19 ⋊ C2×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×D19
SylowC19 ⋊ C2×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C13×D19

Subgroups

subgroupG/H
center, hypercenterC13ΓL(1,𝔽8)×D19
commutator, cosocle, hypocenterC7×C19C2×C3×C13
FrattiniC1G
Fitting, socleC7×C13×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

715 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×D19×AGL(1,𝔽7), D19×ΓL(1,𝔽8)⋊D13, ΓL(1,𝔽8)×D13×D19, …
maximal normal subgroup ofC13×D19×AGL(1,𝔽7), D19×ΓL(1,𝔽8)⋊D13, ΓL(1,𝔽8)×D13×D19, …
maximal quotient ofC13×ΓL(1,𝔽8)×Dic19, C2×C13×ΓL(1,𝔽8)×D19, C13×D19×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 34);