Finite Group Databasebeta

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C2×C3×C16×C121 #72190049

order11616
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7040
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C16×C121
multiplicative(ℤ/12359)ˣ, (ℤ/24718)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8×C11C22×C3×C11
socle, prime radicalC22×C3×C11C8×C11
LCSG ▷ C1
UCSC1 ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C32×C121, C3×C4×C16×C121, C22×C3×C16×C121
maximal normal subgroup ofC2×C3×C32×C121, C3×C4×C16×C121, C22×C3×C16×C121
maximal quotient ofC2×C3×C32×C121, C3×C4×C16×C121, C22×C3×C16×C121
automorphism group ofC17×C727
outer automorphism group ofC17×C727

GAP

Past the SmallGroups library coverage — no SmallGroups id.