Finite Group Databasebeta

← Prev (#24924333) Next (#24924335) →

C11×C13⋊(C52⋊C3) #24924334

order10725
automorphism?
homologyAbelianization (H1) = C3×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×C13⋊(C52⋊C3)
unambiguous semidirect productC13⋊(C11×C52⋊C3)
unambiguous semidirect productC52⋊(C11×C13⋊C3)
unambiguous semidirect product(C11×C13)⋊(C52⋊C3)
unambiguous semidirect product(C52×C11)⋊(C13⋊C3)

Splittings

Fitting, socle, HallC52×C11×C13 ⋊ C3
derived, HallC52×C13 ⋊ C3×C11
HallC52×C11 ⋊ C13⋊C3
HallC11×C13 ⋊ C52⋊C3
SylowC52 ⋊ C11×C13⋊C3
SylowC13 ⋊ C11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC11C13⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C13C3×C11
FrattiniC1G
Fitting, socleC52×C11×C13C3
LCSG ▷ C52×C13
UCSC1 ◁ C11

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1221 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D13⋊(C52⋊C3), C11⋊(D13⋊(C52⋊C3)), D11×C13⋊(C52⋊C3), …
maximal normal subgroup ofC11×D13⋊(C52⋊C3), C11⋊(D13⋊(C52⋊C3)), D11×C13⋊(C52⋊C3), …
maximal quotient ofC2×C11×C13⋊(C52⋊C3), C11×C13⋊(C52⋊C9), C3×C11×C13⋊(C52⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10725, 8);