Finite Group Databasebeta

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C22×C3×C5×C13×C16 #72190823

order12480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 73728
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C5×C13×C16
multiplicative(ℤ/14773)ˣ, (ℤ/15589)ˣ, (ℤ/20043)ˣ, (ℤ/24968)ˣ, (ℤ/29546)ˣ, (ℤ/31178)ˣ, (ℤ/37452)ˣ, (ℤ/40086)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C3×C5×C13
socle, prime radicalC23×C3×C5×C13C8
LCSG ▷ C1
UCSC1 ◁ G

392 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C5×C13×C32, C2×C3×C4×C5×C13×C16, C23×C3×C5×C13×C16
maximal normal subgroup ofC22×C3×C5×C13×C32, C2×C3×C4×C5×C13×C16, C23×C3×C5×C13×C16
maximal quotient ofC22×C3×C5×C13×C32, C2×C3×C4×C5×C13×C16, C23×C3×C5×C13×C16
automorphism group ofC11×C17×C79, C7×C17×C131
outer automorphism group ofC11×C17×C79, C7×C17×C131

GAP

Past the SmallGroups library coverage — no SmallGroups id.