Finite Group Databasebeta

← Prev (#20268798) Next (#20268800) →

C2×C7×C11×C43 #20268799

order6622
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C23×C32×C5×C7 (order 2520) · Inn(G) = C1 · Out(G) = C23×C32×C5×C7
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC6622
abelianC2×C7×C11×C43

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6622 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD13244, Dic6622
Fitting subgroup ofC2×C7×C43×C11⋊C5
socle ofC2×C7×C43×C11⋊C5, D13244, Dic6622, …
maximal subgroup ofC2×C5×C7×C11×C43, C2×C7×C43×C11⋊C5, C7×D5×C11×C43
maximal normal subgroup ofC2×C5×C7×C11×C43, C2×C7×C43×C11⋊C5
maximal quotient ofC2×C5×C7×C11×C43, C7×D5×C11×C43

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6622, 1);