Finite Group Databasebeta

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C23×C52×C31 #72185388

order6200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2419200
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C5

Aliases

abelianC23×C52×C31
multiplicative(ℤ/10263)ˣ, (ℤ/13684)ˣ, (ℤ/20526)ˣ

Subgroups

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

256 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C52×C31, C24×C52×C31, C23×C3×C52×C31, …
maximal normal subgroup ofC22×C4×C52×C31, C24×C52×C31, C23×C3×C52×C31, …
maximal quotient ofC22×C4×C52×C31, C24×C52×C31, C23×C3×C52×C31, …
automorphism group ofC3×C11×C311
outer automorphism group ofC3×C11×C311

GAP

Past the SmallGroups library coverage — no SmallGroups id.