Finite Group Databasebeta

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C2×C3×C4×C11×C41 #72189388

order10824
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C11×C41
multiplicative(ℤ/13535)ˣ, (ℤ/16239)ˣ, (ℤ/21652)ˣ, (ℤ/27070)ˣ, (ℤ/32478)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C11×C41
socle, prime radicalC22×C3×C11×C41C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C42×C11×C41, C2×C3×C8×C11×C41, C22×C3×C4×C11×C41, …
maximal normal subgroup ofC3×C42×C11×C41, C2×C3×C8×C11×C41, C22×C3×C4×C11×C41, …
maximal quotient ofC3×C42×C11×C41, C2×C3×C8×C11×C41, C22×C3×C4×C11×C41, …
automorphism group ofC5×C2707
outer automorphism group ofC5×C2707

GAP

Past the SmallGroups library coverage — no SmallGroups id.