Finite Group Databasebeta

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C22×C7×C16×C27 #72190474

order12096
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 82944
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C7×C16×C27
multiplicative(ℤ/19329)ˣ, (ℤ/24256)ˣ, (ℤ/25772)ˣ, (ℤ/36612)ˣ, (ℤ/38658)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8×C9C23×C3×C7
socle, prime radicalC23×C3×C7C8×C9
LCSG ▷ C1
UCSC1 ◁ G

392 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C7×C27×C32, C2×C4×C7×C16×C27, C23×C7×C16×C27
maximal normal subgroup ofC22×C7×C27×C32, C2×C4×C7×C16×C27, C23×C7×C16×C27
maximal quotient ofC22×C7×C27×C32, C2×C4×C7×C16×C27, C23×C7×C16×C27

GAP

Past the SmallGroups library coverage — no SmallGroups id.