Finite Group Databasebeta

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C7×C19×C11⋊C5 #20300765

order7315
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C5×C7×C19 · Schur multiplier (H2) = C1

Aliases

direct productC7×C19×C11⋊C5
unambiguous semidirect productC11⋊(C5×C7×C19)
unambiguous semidirect product(C7×C11)⋊(C5×C19)
unambiguous semidirect product(C11×C19)⋊(C5×C7)
unambiguous semidirect product(C7×C11×C19)⋊C5

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C5
derived, SylowC11 ⋊ C5×C7×C19
HallC11×C19 ⋊ C5×C7
HallC7×C11 ⋊ C5×C19

Subgroups

subgroupG/H
center, hypercenterC7×C19C11⋊C5
commutator, hypocenterC11C5×C7×C19
FrattiniC1G
Fitting, socleC7×C11×C19C5
LCSG ▷ C11
UCSC1 ◁ C7×C19

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

931 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C7×C19×C11⋊C5, C7×D19×C11⋊C5, C7×C19×AGL(1,𝔽11), …
maximal normal subgroup ofC2×C7×C19×C11⋊C5, C7×D19×C11⋊C5, C7×C19×AGL(1,𝔽11), …
maximal quotient ofC2×C7×C19×C11⋊C5, C3×C7×C19×C11⋊C5, C7×C19×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7315, 2);