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C2×C5×C8×C131 #72189102

order10480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8320
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C5×C8×C131
multiplicative(ℤ/10783)ˣ, (ℤ/11539)ˣ, (ℤ/21566)ˣ, (ℤ/23078)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C5×C131
socle, prime radicalC22×C5×C131C4
LCSG ▷ C1
UCSC1 ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C16×C131, C4×C5×C8×C131, C22×C5×C8×C131, …
maximal normal subgroup ofC2×C5×C16×C131, C4×C5×C8×C131, C22×C5×C8×C131, …
maximal quotient ofC2×C5×C16×C131, C4×C5×C8×C131, C22×C5×C8×C131, …
automorphism group ofC41×C263, C11×C1049
outer automorphism group ofC41×C263, C11×C1049

GAP

Past the SmallGroups library coverage — no SmallGroups id.