Finite Group Databasebeta

← Prev (#22579109) Next (#22579111) →

C22×C32×C5×C72 #22579110

order8820
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2322432
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3×C7

Aliases

abelianC22×C32×C5×C72
multiplicative(ℤ/9073)ˣ, (ℤ/10339)ˣ, (ℤ/18146)ˣ, (ℤ/20678)ˣ

Subgroups

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

600 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8820 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C4×C5×C72, C23×C32×C5×C72, C22×C3×C5×C72×C9, …
maximal normal subgroup ofC2×C32×C4×C5×C72, C23×C32×C5×C72, C22×C3×C5×C72×C9, …
maximal quotient ofC2×C32×C4×C5×C72, C23×C32×C5×C72, C22×C3×C5×C72×C9, …
automorphism group ofC43×C211, C49×C211
outer automorphism group ofC43×C211, C49×C211

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8820, 345);