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D13×#87705 #23780558

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

Aliases

direct productD13×#87705

Splittings

Fitting, socle, derived, HallC7×C13×C19 ⋊ C2×C3
HallC13×#87705 ⋊ C2
HallC7×C19×D13 ⋊ C3
HallC19×D13 ⋊ ΓL(1,𝔽8)
HallC13×C19 ⋊ C2×ΓL(1,𝔽8)
HallC7×D13 ⋊ C19⋊C3
HallC7×C19 ⋊ C3×D13
HallC7×C13 ⋊ C2×C19⋊C3
SylowC19 ⋊ ΓL(1,𝔽8)×D13
SylowC13 ⋊ C2×#87705
SylowC7 ⋊ D13×C19⋊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

376 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#35208953, #35208955, D13×#11716328, …
maximal normal subgroup of#35208953, #35208955, D13×#11716328, …
maximal quotient ofDic13×#87705, C2×D13×#87705, D13×#11924777, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 49);