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C22×C3×C7×C11×C13 #26046459

order12012
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C3×C7×C11×C13
multiplicative(ℤ/12581)ˣ, (ℤ/14021)ˣ, (ℤ/18021)ˣ, (ℤ/18027)ˣ, (ℤ/24028)ˣ, (ℤ/25162)ˣ, (ℤ/28042)ˣ, (ℤ/36042)ˣ, (ℤ/36054)ˣ

Subgroups

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

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12012 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC11×C22⋊#11717941, C11×C22⋊#11717942, C11×C13×C22⋊(C7⋊C9), …
socle ofC22×C7×C9×C11×C13, C11×C22⋊#11717941, C11×C22⋊#11717942, …
maximal subgroup ofC22×C7×C9×C11×C13, C11×C22⋊#11717941, C11×C22⋊#11717942, …
maximal normal subgroup ofC22×C7×C9×C11×C13, C11×C22⋊#11717941, C11×C22⋊#11717942, …
maximal quotient ofC22×C7×C9×C11×C13, C22×C32×C7×C11×C13, C2×C3×D3×C7×C11×C13, …
automorphism group ofC23×C547, C7×C2003
outer automorphism group ofC23×C547, C7×C2003

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 49);