Finite Group Databasebeta

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C2×C3×C16×C103 #72188584

order9888
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6528
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C16×C103
multiplicative(ℤ/10523)ˣ, (ℤ/21046)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C3×C103
socle, prime radicalC22×C3×C103C8
LCSG ▷ C1
UCSC1 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9888 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C32×C103, C3×C4×C16×C103, C22×C3×C16×C103, …
maximal normal subgroup ofC2×C3×C32×C103, C3×C4×C16×C103, C22×C3×C16×C103, …
maximal quotient ofC2×C3×C32×C103, C3×C4×C16×C103, C22×C3×C16×C103, …
automorphism group ofC17×C619
outer automorphism group ofC17×C619

GAP

Past the SmallGroups library coverage — no SmallGroups id.