Finite Group Databasebeta

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C32×C42×C5×C11 #72186831

order7920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 184320
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C4

Aliases

abelianC32×C42×C5×C11
multiplicative(ℤ/8593)ˣ, (ℤ/17186)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C22×C32×C5×C11
socle, prime radicalC22×C32×C5×C11C22
LCSG ▷ C1
UCSC1 ◁ G

360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C4×C5×C8×C11, C2×C32×C42×C5×C11, C33×C42×C5×C11, …
maximal normal subgroup ofC32×C4×C5×C8×C11, C2×C32×C42×C5×C11, C33×C42×C5×C11, …
maximal quotient ofC32×C4×C5×C8×C11, C2×C32×C42×C5×C11, C33×C42×C5×C11, …
automorphism group ofC13×C661
outer automorphism group ofC13×C661

GAP

Past the SmallGroups library coverage — no SmallGroups id.