Finite Group Databasebeta

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C2×C3×C4×C11×C53 #72192182

order13992
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8320
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C11×C53
multiplicative(ℤ/16331)ˣ, (ℤ/17495)ˣ, (ℤ/20991)ˣ, (ℤ/20997)ˣ, (ℤ/27988)ˣ, (ℤ/32662)ˣ, (ℤ/34990)ˣ, (ℤ/41982)ˣ, (ℤ/41994)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C11×C53
socle, prime radicalC22×C3×C11×C53C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13992 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C42×C11×C53, C2×C3×C8×C11×C53, C22×C3×C4×C11×C53
maximal normal subgroup ofC3×C42×C11×C53, C2×C3×C8×C11×C53, C22×C3×C4×C11×C53
maximal quotient ofC3×C42×C11×C53, C2×C3×C8×C11×C53, C22×C3×C4×C11×C53
automorphism group ofC7×C2333, C5×C3499
outer automorphism group ofC7×C2333, C5×C3499

GAP

Past the SmallGroups library coverage — no SmallGroups id.