Finite Group Databasebeta

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C23×C4×C7×C53 #72190304

order11872
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6709248
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C4×C7×C53
multiplicative(ℤ/24824)ˣ, (ℤ/29720)ˣ, (ℤ/35664)ˣ, (ℤ/37236)ˣ, (ℤ/44580)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C7×C53
socle, prime radicalC24×C7×C53C2
LCSG ▷ C1
UCSC1 ◁ G

472 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11872 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C7×C8×C53, C22×C42×C7×C53, C24×C4×C7×C53
maximal normal subgroup ofC23×C7×C8×C53, C22×C42×C7×C53, C24×C4×C7×C53
maximal quotient ofC23×C7×C8×C53, C22×C42×C7×C53, C24×C4×C7×C53
automorphism group ofC8×C29×C107, C5×C8×C743
outer automorphism group ofC8×C29×C107, C5×C8×C743

GAP

Past the SmallGroups library coverage — no SmallGroups id.