Finite Group Databasebeta

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C22×C4×C11×C64 #72189759

order11264
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 15728640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C4×C11×C64
multiplicative(ℤ/29440)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C32C24×C11
socle, prime radicalC24×C11C2×C32
LCSG ▷ C1
UCSC1 ◁ G

1546 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C11×C128, C22×C8×C11×C64, C2×C42×C11×C64, …
maximal normal subgroup ofC22×C4×C11×C128, C22×C8×C11×C64, C2×C42×C11×C64, …
maximal quotient ofC22×C4×C11×C128, C22×C8×C11×C64, C2×C42×C11×C64, …
automorphism group ofC5×C23×C256
outer automorphism group ofC5×C23×C256

GAP

Past the SmallGroups library coverage — no SmallGroups id.