Finite Group Databasebeta

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C4×C5×C82×C11 #72192242

order14080
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 31457280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C42×C8

Aliases

abelianC4×C5×C82×C11
multiplicative(ℤ/18245)ˣ, (ℤ/36490)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C42C23×C5×C11
socle, prime radicalC23×C5×C11C2×C42
LCSG ▷ C1
UCSC1 ◁ G

1500 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C8×C11×C16, C5×C83×C11, C2×C4×C5×C82×C11
maximal normal subgroup ofC4×C5×C8×C11×C16, C5×C83×C11, C2×C4×C5×C82×C11
maximal quotient ofC4×C5×C8×C11×C16, C5×C83×C11, C2×C4×C5×C82×C11

GAP

Past the SmallGroups library coverage — no SmallGroups id.