Finite Group Databasebeta

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C22×C5×C16×C27 #72187485

order8640
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 55296
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C5×C16×C27
multiplicative(ℤ/13821)ˣ, (ℤ/14289)ˣ, (ℤ/15147)ˣ, (ℤ/17288)ˣ, (ℤ/17344)ˣ, (ℤ/18428)ˣ, (ℤ/19052)ˣ, (ℤ/25932)ˣ, (ℤ/27642)ˣ, (ℤ/28578)ˣ, (ℤ/30294)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8×C9C23×C3×C5
socle, prime radicalC23×C3×C5C8×C9
LCSG ▷ C1
UCSC1 ◁ G

392 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8640 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C27×C32, C2×C4×C5×C16×C27, C23×C5×C16×C27, …
maximal normal subgroup ofC22×C5×C27×C32, C2×C4×C5×C16×C27, C23×C5×C16×C27, …
maximal quotient ofC22×C5×C27×C32, C2×C4×C5×C16×C27, C23×C5×C16×C27, …
automorphism group ofC11×C17×C81, C2×C11×C17×C81
outer automorphism group ofC11×C17×C81, C2×C11×C17×C81

GAP

Past the SmallGroups library coverage — no SmallGroups id.