Finite Group Databasebeta

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C2×C11×C16×C17 #72185178

order5984
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C11×C16×C17
multiplicative(ℤ/6647)ˣ, (ℤ/13294)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C11×C17
socle, prime radicalC22×C11×C17C8
LCSG ▷ C1
UCSC1 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5984 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C17×C32, C4×C11×C16×C17, C22×C11×C16×C17, …
maximal normal subgroup ofC2×C11×C17×C32, C4×C11×C16×C17, C22×C11×C16×C17, …
maximal quotient ofC2×C11×C17×C32, C4×C11×C16×C17, C22×C11×C16×C17, …
automorphism group ofC23×C289
outer automorphism group ofC23×C289

GAP

Past the SmallGroups library coverage — no SmallGroups id.