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C22×C9×C11×C29 #26039780

order11484
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C9×C11×C29
multiplicative(ℤ/11741)ˣ, (ℤ/12029)ˣ, (ℤ/17229)ˣ, (ℤ/22972)ˣ, (ℤ/23482)ˣ, (ℤ/24058)ˣ, (ℤ/34458)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C22×C3×C11×C29
socle, prime radicalC22×C3×C11×C29C3
LCSG ▷ C1
UCSC1 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11484 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C9×C11×C29, C23×C9×C11×C29
maximal normal subgroup ofC2×C4×C9×C11×C29, C23×C9×C11×C29
maximal quotient ofC2×C4×C9×C11×C29, C23×C9×C11×C29
automorphism group ofC59×C199, C23×C523
outer automorphism group ofC59×C199, C23×C523

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11484, 9);