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C22×C5×C9×C59 #24902866

order10620
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8352
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C5×C9×C59
multiplicative(ℤ/11693)ˣ, (ℤ/23386)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C22×C3×C5×C59
socle, prime radicalC22×C3×C5×C59C3
LCSG ▷ C1
UCSC1 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10620 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C5×C9×C59, C23×C5×C9×C59, C22×C5×C27×C59, …
maximal normal subgroup ofC2×C4×C5×C9×C59, C23×C5×C9×C59, C22×C5×C27×C59, …
maximal quotient ofC2×C4×C5×C9×C59, C23×C5×C9×C59, C22×C5×C27×C59, …
automorphism group ofC11×C1063
outer automorphism group ofC11×C1063

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10620, 9);