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C13×#11716325 #23780583

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

Aliases

direct productC13×#11716325

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C13
HallC13×#87704 ⋊ C2
HallC13×D7×C19 ⋊ C3
Hall#87704 ⋊ C2×C13
HallD7×C19 ⋊ C3×C13
HallC13×C19 ⋊ AGL(1,𝔽7)
HallC13×D7 ⋊ C19⋊C3
HallC7×C13 ⋊ C2×C19⋊C3
SylowC19 ⋊ C13×AGL(1,𝔽7)
HallD7 ⋊ C13×C19⋊C3
SylowC7 ⋊ C2×C13×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC13#11716325
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

481 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×#11716321⋊C2, #11716325⋊D13, D13×#11716325, …
maximal normal subgroup ofC13×#11716321⋊C2, #11716325⋊D13, D13×#11716325, …
maximal quotient ofC13×#13097586, C2×C13×#11716325, C13×#14558784, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 74);