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C22×C32×C173 #20262004

order6228
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 49536
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C32×C173
multiplicative(ℤ/7273)ˣ, (ℤ/9351)ˣ, (ℤ/14546)ˣ, (ℤ/18702)ˣ

Subgroups

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

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6228 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C5×C173, C2×C32×D5×C173, C2×C32×C4×C173, …
maximal normal subgroup ofC22×C32×C5×C173, C2×C32×C4×C173, C23×C32×C173, …
maximal quotient ofC22×C32×C5×C173, C2×C32×D5×C173, C2×C32×C4×C173, …
automorphism group ofC7×C1039, C9×C1039
outer automorphism group ofC7×C1039, C9×C1039

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6228, 19);