Finite Group Databasebeta

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C3×C4×C5×C13×C16 #72190821

order12480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 24576
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC3×C4×C5×C13×C16
multiplicative(ℤ/12773)ˣ, (ℤ/15605)ˣ, (ℤ/25546)ˣ, (ℤ/31210)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C22×C3×C5×C13
socle, prime radicalC22×C3×C5×C13C2×C8
LCSG ▷ C1
UCSC1 ◁ G

232 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 ofC3×C4×C5×C13×C32, C3×C5×C8×C13×C16, C2×C3×C4×C5×C13×C16
maximal normal subgroup ofC3×C4×C5×C13×C32, C3×C5×C8×C13×C16, C2×C3×C4×C5×C13×C16
maximal quotient ofC3×C4×C5×C13×C32, C3×C5×C8×C13×C16, C2×C3×C4×C5×C13×C16
automorphism group ofC53×C241, C5×C3121
outer automorphism group ofC53×C241, C5×C3121

GAP

Past the SmallGroups library coverage — no SmallGroups id.