Finite Group Databasebeta

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C4×C7×C16×C17 #72186554

order7616
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 24576
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C7×C16×C17
multiplicative(ℤ/8381)ˣ, (ℤ/16762)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C22×C7×C17
socle, prime radicalC22×C7×C17C2×C8
LCSG ▷ C1
UCSC1 ◁ G

116 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C7×C17×C32, C7×C8×C16×C17, C2×C4×C7×C16×C17, …
maximal normal subgroup ofC4×C7×C17×C32, C7×C8×C16×C17, C2×C4×C7×C16×C17, …
maximal quotient ofC4×C7×C17×C32, C7×C8×C16×C17, C2×C4×C7×C16×C17, …
automorphism group ofC29×C289
outer automorphism group ofC29×C289

GAP

Past the SmallGroups library coverage — no SmallGroups id.