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C2×C9×C11×C64 #72191007

order12672
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7680
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C9×C11×C64
multiplicative(ℤ/13271)ˣ, (ℤ/19011)ˣ, (ℤ/25348)ˣ, (ℤ/26542)ˣ, (ℤ/38022)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C32C22×C3×C11
socle, prime radicalC22×C3×C11C3×C32
LCSG ▷ C1
UCSC1 ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12672 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C9×C11×C128, C4×C9×C11×C64, C22×C9×C11×C64
maximal normal subgroup ofC2×C9×C11×C128, C4×C9×C11×C64, C22×C9×C11×C64
maximal quotient ofC2×C9×C11×C128, C4×C9×C11×C64, C22×C9×C11×C64
automorphism group ofC23×C577
outer automorphism group ofC23×C577

GAP

Past the SmallGroups library coverage — no SmallGroups id.