Finite Group Databasebeta

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C4×C72×C64 #72190885

order12544
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2064384
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4×C7

Aliases

abelianC4×C72×C64
multiplicative(ℤ/13021)ˣ, (ℤ/26042)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C32C22×C72
socle, prime radicalC22×C72C2×C32
LCSG ▷ C1
UCSC1 ◁ G

430 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12544 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C72×C128, C72×C8×C64, C2×C4×C72×C64
maximal normal subgroup ofC4×C72×C128, C72×C8×C64, C2×C4×C72×C64
maximal quotient ofC4×C72×C128, C72×C8×C64, C2×C4×C72×C64
automorphism group ofC29×C449
outer automorphism group ofC29×C449

GAP

Past the SmallGroups library coverage — no SmallGroups id.