Finite Group Databasebeta

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C3×C43×C5×C11 #72189155

order10560
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6881280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C43

Aliases

abelianC3×C43×C5×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23C23×C3×C5×C11
socle, prime radicalC23×C3×C5×C11C23
LCSG ▷ C1
UCSC1 ◁ G

1032 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10560 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C42×C5×C8×C11, C2×C3×C43×C5×C11, C43×C5×C9×C11, …
maximal normal subgroup ofC3×C42×C5×C8×C11, C2×C3×C43×C5×C11, C43×C5×C9×C11, …
maximal quotient ofC3×C42×C5×C8×C11, C2×C3×C43×C5×C11, C43×C5×C9×C11, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.