Finite Group Databasebeta

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C22×C3×C72×C16 #72188173

order9408
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3096576
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C7

Aliases

abelianC22×C3×C72×C16
multiplicative(ℤ/14577)ˣ, (ℤ/16611)ˣ, (ℤ/19436)ˣ, (ℤ/22148)ˣ, (ℤ/29154)ˣ, (ℤ/33222)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C3×C72
socle, prime radicalC23×C3×C72C8
LCSG ▷ C1
UCSC1 ◁ G

980 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9408 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C72×C32, C2×C3×C4×C72×C16, C23×C3×C72×C16, …
maximal normal subgroup ofC22×C3×C72×C32, C2×C3×C4×C72×C16, C23×C3×C72×C16, …
maximal quotient ofC22×C3×C72×C32, C2×C3×C4×C72×C16, C23×C3×C72×C16, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.