Finite Group Databasebeta

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C22×C3×C5×C162 #72193361

order15360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 301989888
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C16

Aliases

abelianC22×C3×C5×C162
multiplicative(ℤ/32776)ˣ, (ℤ/33728)ˣ, (ℤ/46272)ˣ, (ℤ/49164)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC82C24×C3×C5
socle, prime radicalC24×C3×C5C82
LCSG ▷ C1
UCSC1 ◁ G

6292 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C5×C16×C32, C23×C3×C5×C162, C2×C3×C4×C5×C162
maximal normal subgroup ofC22×C3×C5×C16×C32, C23×C3×C5×C162, C2×C3×C4×C5×C162
maximal quotient ofC22×C3×C5×C16×C32, C23×C3×C5×C162, C2×C3×C4×C5×C162

GAP

Past the SmallGroups library coverage — no SmallGroups id.