Finite Group Databasebeta

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C22×C3×C16×C53 #72188794

order10176
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 79872
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C16×C53
multiplicative(ℤ/12733)ˣ, (ℤ/16371)ˣ, (ℤ/25466)ˣ, (ℤ/32742)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C3×C53
socle, prime radicalC23×C3×C53C8
LCSG ▷ C1
UCSC1 ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10176 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C32×C53, C2×C3×C4×C16×C53, C23×C3×C16×C53, …
maximal normal subgroup ofC22×C3×C32×C53, C2×C3×C4×C16×C53, C23×C3×C16×C53, …
maximal quotient ofC22×C3×C32×C53, C2×C3×C4×C16×C53, C23×C3×C16×C53, …
automorphism group ofC7×C17×C107
outer automorphism group ofC7×C17×C107

GAP

Past the SmallGroups library coverage — no SmallGroups id.