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C2×C5×C11×C49 #19129114

order5390
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C4×C5×C7 (order 1680) · Inn(G) = C1 · Out(G) = C22×C3×C4×C5×C7
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC5390
abelianC2×C5×C11×C49

Subgroups

subgroupG/H
centerGC1
commutatorC1G
FrattiniC7C2×C5×C7×C11
socleC2×C5×C7×C11C7
LCSG ▷ C1
UCSC1 ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5390 conjugacy classes. The character table is too large to display.

Relationships

center ofC5×C11×Dic3×C49, C2×C5×D3×C11×C49
Fitting subgroup ofC2×C5×C11×C49⋊C3, C2×C49×C11⋊C25, C2×C5×C49×C11⋊C5, …
maximal subgroup ofC2×C3×C5×C11×C49, C2×C5×C11×C49⋊C3, C5×D3×C11×C49, …
maximal normal subgroup ofC2×C3×C5×C11×C49, C2×C5×C11×C49⋊C3, C2×C11×C25×C49, …
maximal quotient ofC2×C3×C5×C11×C49, C5×D3×C11×C49, C2×C11×C25×C49, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5390, 1);