Finite Group Databasebeta

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C3×C5×C162 #72183400

order3840
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 196608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C16

Aliases

abelianC3×C5×C162
multiplicative(ℤ/4097)ˣ, (ℤ/8194)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC82C22×C3×C5
socle, prime radicalC22×C3×C5C82
LCSG ▷ C1
UCSC1 ◁ G

332 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C16×C32, C2×C3×C5×C162, C5×C9×C162, …
maximal normal subgroup ofC3×C5×C16×C32, C2×C3×C5×C162, C5×C9×C162, …
maximal quotient ofC3×C5×C16×C32, C2×C3×C5×C162, C5×C9×C162, …
automorphism group ofC17×C241, C2×C17×C241
outer automorphism group ofC17×C241, C2×C17×C241

GAP

Past the SmallGroups library coverage — no SmallGroups id.