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D19×#63270 #23780546

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

Aliases

direct productD19×#63270

Splittings

Fitting, socle, derived, HallC7×C13×C19 ⋊ C2×C3
HallC19×#63270 ⋊ C2
HallC7×C13×D19 ⋊ C3
HallC13×D19 ⋊ ΓL(1,𝔽8)
HallC7×D19 ⋊ C13⋊C3
HallC13×C19 ⋊ C2×ΓL(1,𝔽8)
HallC7×C19 ⋊ C2×C13⋊C3
HallC7×C13 ⋊ C3×D19
SylowC19 ⋊ C2×#63270
SylowC13 ⋊ ΓL(1,𝔽8)×D19
SylowC7 ⋊ D19×C13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C19C2×C3
LCSG ▷ C7×C13×C19
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

363 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19×#10587722, D19×#10587720, D19×#10587716, …
maximal normal subgroup ofD19×#10587722, D19×#10587720, D19×#10587716, …
maximal quotient ofDic19×#63270, C2×D19×#63270, D19×#11717941, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 37);