Finite Group Databasebeta

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C2×C4×C11×C128 #72189754

order11264
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 327680
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C4×C11×C128
multiplicative(ℤ/21135)ˣ, (ℤ/22544)ˣ, (ℤ/28180)ˣ, (ℤ/42270)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C64C23×C11
socle, prime radicalC23×C11C2×C64
LCSG ▷ C1
UCSC1 ◁ G

378 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 ofC2×C4×C11×C256, C42×C11×C128, C2×C8×C11×C128, …
maximal normal subgroup ofC2×C4×C11×C256, C42×C11×C128, C2×C8×C11×C128, …
maximal quotient ofC2×C4×C11×C256, C42×C11×C128, C2×C8×C11×C128, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.