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C22×C32×C5×C43 #21440893

order7740
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 48384
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C32×C5×C43
multiplicative(ℤ/9037)ˣ, (ℤ/11619)ˣ, (ℤ/18074)ˣ, (ℤ/23238)ˣ

Subgroups

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

120 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×C32×C4×C5×C43, C23×C32×C5×C43, C22×C3×C5×C9×C43, …
maximal normal subgroup ofC2×C32×C4×C5×C43, C23×C32×C5×C43, C22×C3×C5×C9×C43, …
maximal quotient ofC2×C32×C4×C5×C43, C23×C32×C5×C43, C22×C3×C5×C9×C43, …
automorphism group ofC7×C1291
outer automorphism group ofC7×C1291

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7740, 61);