Finite Group Databasebeta

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C4×C7×C11×C19 #19154402

order5852
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C24×C3×C5×C9 (order 2160) · Inn(G) = C1 · Out(G) = C24×C3×C5×C9
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC5852
abelianC4×C7×C11×C19

Subgroups

subgroupG/H
centerGC1
commutatorC1G
FrattiniC2C2×C7×C11×C19
socleC2×C7×C11×C19C2
LCSG ▷ C1
UCSC1 ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5852 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC4×C7×C11×C19⋊C3, C4×C11×C19×ΓL(1,𝔽8), C4×C11×#87704, …
maximal subgroup ofC3×C4×C7×C11×C19, C4×C7×C11×C19⋊C3, C4×C11×C19×ΓL(1,𝔽8), …
maximal normal subgroup ofC3×C4×C7×C11×C19, C4×C7×C11×C19⋊C3, C4×C11×C19×ΓL(1,𝔽8), …
maximal quotient ofC3×C4×C7×C11×C19, C7×C11×Dic3×C19, C4×C5×C7×C11×C19, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5852, 1);