Finite Group Databasebeta

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C23×C3×C52×C23 #72191978

order13800
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3548160
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C5

Aliases

abelianC23×C3×C52×C23
multiplicative(ℤ/16027)ˣ, (ℤ/22803)ˣ, (ℤ/30404)ˣ, (ℤ/32054)ˣ, (ℤ/45606)ˣ

Subgroups

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

512 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C52×C23, C24×C3×C52×C23
maximal normal subgroup ofC22×C3×C4×C52×C23, C24×C3×C52×C23
maximal quotient ofC22×C3×C4×C52×C23, C24×C3×C52×C23
automorphism group ofC11×C31×C47
outer automorphism group ofC11×C31×C47

GAP

Past the SmallGroups library coverage — no SmallGroups id.