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C22×C5×C11×C49 #24924700

order10780
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C5×C11×C49
multiplicative(ℤ/11293)ˣ, (ℤ/22586)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7C22×C5×C7×C11
socle, prime radicalC22×C5×C7×C11C7
LCSG ▷ C1
UCSC1 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10780 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC22×C5×C11×C49⋊C3, C5×C11×A4×C49, C5×C11×C22⋊(C49⋊C3)
maximal subgroup ofC22×C3×C5×C11×C49, C22×C5×C11×C49⋊C3, C5×C11×A4×C49, …
maximal normal subgroup ofC22×C3×C5×C11×C49, C22×C5×C11×C49⋊C3, C5×C11×A4×C49, …
maximal quotient ofC22×C3×C5×C11×C49, C2×C5×D3×C11×C49, C2×C4×C5×C11×C49, …
automorphism group ofC23×C491
outer automorphism group ofC23×C491

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 13);