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C13×#11716321 #23780544

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

Aliases

direct productC13×#11716321

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C13
HallC13×#87704 ⋊ C2
HallC7×C13×D19 ⋊ C3
HallC13×D19 ⋊ ΓL(1,𝔽8)
Hall#87704 ⋊ C2×C13
HallC7×D19 ⋊ C3×C13
HallC13×C19 ⋊ C2×ΓL(1,𝔽8)
HallC7×C13 ⋊ D19⋊C3
HallD19 ⋊ C13×ΓL(1,𝔽8)
SylowC19 ⋊ C2×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C13×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC13#11716321
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

403 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×#11716321⋊C2, #11716321⋊D13, D13×#11716321, …
maximal normal subgroup ofC13×#11716321⋊C2, #11716321⋊D13, D13×#11716321, …
maximal quotient ofC13×#13097582, C2×C13×#11716321, C13×#14558780, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 35);