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C22×C3×C5×C11×C13 #22575065

order8580
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C3×C5×C11×C13
multiplicative(ℤ/8777)ˣ, (ℤ/9449)ˣ, (ℤ/9559)ˣ, (ℤ/17554)ˣ, (ℤ/18898)ˣ, (ℤ/19118)ˣ

Subgroups

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

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8580 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC5×C11×C22⋊(C13⋊C9), C5×C11×C13×C22⋊C9, C22×C5×C11×C13⋊C9, …
socle ofC22×C5×C9×C11×C13, C5×C11×C22⋊(C13⋊C9), C5×C11×C13×C22⋊C9, …
maximal subgroup ofC22×C5×C9×C11×C13, C5×C11×C22⋊(C13⋊C9), C5×C11×C13×C22⋊C9, …
maximal normal subgroup ofC22×C5×C9×C11×C13, C5×C11×C22⋊(C13⋊C9), C5×C11×C13×C22⋊C9, …
maximal quotient ofC22×C5×C9×C11×C13, C22×C32×C5×C11×C13, C2×C3×C5×D3×C11×C13, …
automorphism group ofC67×C131, C11×C859, C79×C121
outer automorphism group ofC67×C131, C11×C859, C79×C121

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 37);