Finite Group Databasebeta

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C2×C11×C16×C27 #72188237

order9504
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C11×C16×C27
multiplicative(ℤ/9959)ˣ, (ℤ/19918)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8×C9C22×C3×C11
socle, prime radicalC22×C3×C11C8×C9
LCSG ▷ C1
UCSC1 ◁ G

112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9504 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C27×C32, C4×C11×C16×C27, C22×C11×C16×C27, …
maximal normal subgroup ofC2×C11×C27×C32, C4×C11×C16×C27, C22×C11×C16×C27, …
maximal quotient ofC2×C11×C27×C32, C4×C11×C16×C27, C22×C11×C16×C27, …
automorphism group ofC23×C433
outer automorphism group ofC23×C433

GAP

Past the SmallGroups library coverage — no SmallGroups id.