Finite Group Databasebeta

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C22×C42×C11×C16 #72189773

order11264
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 48318382080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C27×C43

Aliases

abelianC22×C42×C11×C16
multiplicative(ℤ/31280)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C8C25×C11
socle, prime radicalC25×C11C22×C8
LCSG ▷ C1
UCSC1 ◁ G

18282 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C42×C11×C32, C22×C4×C8×C11×C16, C2×C43×C11×C16, …
maximal normal subgroup ofC22×C42×C11×C32, C22×C4×C8×C11×C16, C2×C43×C11×C16, …
maximal quotient ofC22×C42×C11×C32, C22×C4×C8×C11×C16, C2×C43×C11×C16, …
automorphism group ofC5×C16×C17×C23
outer automorphism group ofC5×C16×C17×C23

GAP

Past the SmallGroups library coverage — no SmallGroups id.