Finite Group Databasebeta

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C22×C11×C16×C23 #72194152

order16192
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 168960
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C11×C16×C23
multiplicative(ℤ/18377)ˣ, (ℤ/26979)ˣ, (ℤ/32392)ˣ, (ℤ/33856)ˣ, (ℤ/35972)ˣ, (ℤ/36754)ˣ, (ℤ/48588)ˣ, (ℤ/53958)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C11×C23
socle, prime radicalC23×C11×C23C8
LCSG ▷ C1
UCSC1 ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16192 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C11×C23×C32, C2×C4×C11×C16×C23, C23×C11×C16×C23
maximal normal subgroup ofC22×C11×C23×C32, C2×C4×C11×C16×C23, C23×C11×C16×C23
maximal quotient ofC22×C11×C23×C32, C2×C4×C11×C16×C23, C23×C11×C16×C23

GAP

Past the SmallGroups library coverage — no SmallGroups id.