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C22×C32×C7×C37 #22605192

order9324
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 62208
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C32×C7×C37
multiplicative(ℤ/9589)ˣ, (ℤ/10927)ˣ, (ℤ/19178)ˣ, (ℤ/21854)ˣ

Subgroups

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

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9324 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C4×C7×C37, C23×C32×C7×C37, C22×C3×C7×C9×C37, …
maximal normal subgroup ofC2×C32×C4×C7×C37, C23×C32×C7×C37, C22×C3×C7×C9×C37, …
maximal quotient ofC2×C32×C4×C7×C37, C23×C32×C7×C37, C22×C3×C7×C9×C37, …
automorphism group ofC43×C223, C49×C223
outer automorphism group ofC43×C223, C49×C223

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9324, 137);