Finite Group Databasebeta

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C2×C3×C16×C47 #72183995

order4512
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2944
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C16×C47
multiplicative(ℤ/4811)ˣ, (ℤ/9622)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C3×C47
socle, prime radicalC22×C3×C47C8
LCSG ▷ C1
UCSC1 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C32×C47, C3×C4×C16×C47, C22×C3×C16×C47, …
maximal normal subgroup ofC2×C3×C32×C47, C3×C4×C16×C47, C22×C3×C16×C47, …
maximal quotient ofC2×C3×C32×C47, C3×C4×C16×C47, C22×C3×C16×C47, …
automorphism group ofC17×C283, C2×C17×C283
outer automorphism group ofC17×C283, C2×C17×C283

GAP

Past the SmallGroups library coverage — no SmallGroups id.