Finite Group Databasebeta

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C5×C82×C11 #72183174

order3520
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 61440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C8

Aliases

abelianC5×C82×C11
multiplicative(ℤ/3649)ˣ, (ℤ/7298)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC42C22×C5×C11
socle, prime radicalC22×C5×C11C42
LCSG ▷ C1
UCSC1 ◁ G

148 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C8×C11×C16, C2×C5×C82×C11, C3×C5×C82×C11, …
maximal normal subgroup ofC5×C8×C11×C16, C2×C5×C82×C11, C3×C5×C82×C11, …
maximal quotient ofC5×C8×C11×C16, C2×C5×C82×C11, C3×C5×C82×C11, …
automorphism group ofC41×C89, C2×C41×C89
outer automorphism group ofC41×C89, C2×C41×C89

GAP

Past the SmallGroups library coverage — no SmallGroups id.