Finite Group Databasebeta

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C32×C42×C5×C13 #72188141

order9360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 221184
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C4

Aliases

abelianC32×C42×C5×C13
multiplicative(ℤ/9577)ˣ, (ℤ/10309)ˣ, (ℤ/19154)ˣ, (ℤ/20618)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C22×C32×C5×C13
socle, prime radicalC22×C32×C5×C13C22
LCSG ▷ C1
UCSC1 ◁ G

360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C4×C5×C8×C13, C2×C32×C42×C5×C13, C3×C42×C5×C9×C13, …
maximal normal subgroup ofC32×C4×C5×C8×C13, C2×C32×C42×C5×C13, C3×C42×C5×C9×C13, …
maximal quotient ofC32×C4×C5×C8×C13, C2×C32×C42×C5×C13, C3×C42×C5×C9×C13, …
automorphism group ofC61×C157, C61×C169
outer automorphism group ofC61×C157, C61×C169

GAP

Past the SmallGroups library coverage — no SmallGroups id.