Finite Group Databasebeta

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C2×C8×C11×C71 #72190834

order12496
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 11200
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C8×C11×C71
multiplicative(ℤ/13087)ˣ, (ℤ/26174)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C11×C71
socle, prime radicalC22×C11×C71C4
LCSG ▷ C1
UCSC1 ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12496 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C16×C71, C4×C8×C11×C71, C22×C8×C11×C71
maximal normal subgroup ofC2×C11×C16×C71, C4×C8×C11×C71, C22×C8×C11×C71
maximal quotient ofC2×C11×C16×C71, C4×C8×C11×C71, C22×C8×C11×C71
automorphism group ofC23×C569
outer automorphism group ofC23×C569

GAP

Past the SmallGroups library coverage — no SmallGroups id.