Finite Group Databasebeta

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C2×C11×C19×D13 #24925893

order10868
isoclinismisoclinic class of D13
automorphism?
homologyAbelianization (H1) = C22×C11×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C19×D13
unambiguous semidirect productC13⋊(C22×C11×C19)
unambiguous semidirect product(C2×C13)⋊(C2×C11×C19)

Splittings

Fitting, socleC2×C11×C13×C19 ⋊ C2
derived, SylowC13 ⋊ C22×C11×C19
HallC11×C13×C19 ⋊ C22
HallC13×C19 ⋊ C22×C11
HallC11×C13 ⋊ C22×C19

Subgroups

subgroupG/H
center, hypercenterC2×C11×C19D13
commutator, cosocle, hypocenterC13C22×C11×C19
FrattiniC1G
Fitting, socleC2×C11×C13×C19C2
LCSG ▷ C13
UCSC1 ◁ C2×C11×C19

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3344 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C19×D13⋊C3, C2×C11×#13093364, C2×C11×#13093365, …
maximal normal subgroup ofC2×C11×C19×D13⋊C3, C2×C11×#13093364, C2×C11×#13093365, …
maximal quotient ofD3×C11×C19×D13, C2×C3×C11×C19×D13, C2×C11×C19×D39

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10868, 26);