Finite Group Databasebeta

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C2×C3×C5×C13×C16 #72185404

order6240
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3072
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C5×C13×C16
multiplicative(ℤ/9363)ˣ, (ℤ/12484)ˣ, (ℤ/18726)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C3×C5×C13
socle, prime radicalC22×C3×C5×C13C8
LCSG ▷ C1
UCSC1 ◁ G

112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6240 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C13×C32, C3×C4×C5×C13×C16, C22×C3×C5×C13×C16, …
maximal normal subgroup ofC2×C3×C5×C13×C32, C3×C4×C5×C13×C16, C22×C3×C5×C13×C16, …
maximal quotient ofC2×C3×C5×C13×C32, C3×C4×C5×C13×C16, C22×C3×C5×C13×C16, …
automorphism group ofC3×C3121
outer automorphism group ofC3×C3121

GAP

Past the SmallGroups library coverage — no SmallGroups id.