Finite Group Databasebeta

← Prev (#22554891) Next (#22554893) →

C22×C32×C5×C47 #22554892

order8460
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 52992
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C32×C5×C47
multiplicative(ℤ/8773)ˣ, (ℤ/17546)ˣ

Subgroups

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

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8460 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C4×C5×C47, C23×C32×C5×C47, C22×C3×C5×C9×C47, …
maximal normal subgroup ofC2×C32×C4×C5×C47, C23×C32×C5×C47, C22×C3×C5×C9×C47, …
maximal quotient ofC2×C32×C4×C5×C47, C23×C32×C5×C47, C22×C3×C5×C9×C47, …
automorphism group ofC31×C283
outer automorphism group ofC31×C283

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8460, 41);