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C22×C5×C9×C43 #21440845

order7740
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6048
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C5×C9×C43
multiplicative(ℤ/8189)ˣ, (ℤ/11637)ˣ, (ℤ/16378)ˣ, (ℤ/23274)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
FrattiniC3C22×C3×C5×C43
socleC22×C3×C5×C43C3
LCSG ▷ C1
UCSC1 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7740 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C5×C9×C43, C23×C5×C9×C43, C22×C5×C27×C43, …
maximal normal subgroup ofC2×C4×C5×C9×C43, C23×C5×C9×C43, C22×C5×C27×C43, …
maximal quotient ofC2×C4×C5×C9×C43, C23×C5×C9×C43, C22×C5×C27×C43, …
automorphism group ofC19×C431, C2×C27×C431
outer automorphism group ofC19×C431, C2×C27×C431

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7740, 13);