Finite Group Databasebeta

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C2×C32×C4×C8×C11 #72185494

order6336
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 983040
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4

Aliases

abelianC2×C32×C4×C8×C11
multiplicative(ℤ/8099)ˣ, (ℤ/10413)ˣ, (ℤ/16198)ˣ, (ℤ/20826)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C23×C32×C11
socle, prime radicalC23×C32×C11C2×C4
LCSG ▷ C1
UCSC1 ◁ G

972 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6336 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C4×C11×C16, C2×C32×C82×C11, C32×C42×C8×C11, …
maximal normal subgroup ofC2×C32×C4×C11×C16, C2×C32×C82×C11, C32×C42×C8×C11, …
maximal quotient ofC2×C32×C4×C11×C16, C2×C32×C82×C11, C32×C42×C8×C11, …
automorphism group ofC7×C13×C89, C9×C13×C89
outer automorphism group ofC7×C13×C89, C9×C13×C89

GAP

Past the SmallGroups library coverage — no SmallGroups id.