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C19×#10587717 #23780562

order10374
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×#10587717

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C19
HallC19×#63271 ⋊ C2
HallC7×C19×D13 ⋊ C3
HallC19×D13 ⋊ ΓL(1,𝔽8)
Hall#63271 ⋊ C2×C19
HallC13×C19 ⋊ C2×ΓL(1,𝔽8)
HallC7×D13 ⋊ C3×C19
HallC7×C19 ⋊ D13⋊C3
HallD13 ⋊ C19×ΓL(1,𝔽8)
SylowC13 ⋊ C2×C19×ΓL(1,𝔽8)
SylowC7 ⋊ C19×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC19#10587717
commutator, cosocle, hypocenterC7×C13C2×C3×C19
FrattiniC1G
Fitting, socleC7×C13×C19C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

456 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#11763984, #35208920, C19×#10587717⋊C2, …
maximal normal subgroup ofC19×#11763984, #35208920, C19×#10587717⋊C2, …
maximal quotient ofC19×#11763958, C2×C19×#10587717, C19×#13109897, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 53);