Finite Group Databasebeta

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C4×C16×C169 #72189369

order10816
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 39936
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C16×C169
multiplicative(ℤ/11509)ˣ, (ℤ/23018)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8×C13C22×C13
socle, prime radicalC22×C13C2×C8×C13
LCSG ▷ C1
UCSC1 ◁ G

87 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10816 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C32×C169, C8×C16×C169, C2×C4×C16×C169, …
maximal normal subgroup ofC4×C32×C169, C8×C16×C169, C2×C4×C16×C169, …
maximal quotient ofC4×C32×C169, C8×C16×C169, C2×C4×C16×C169, …
automorphism group ofC17×C677
outer automorphism group ofC17×C677

GAP

Past the SmallGroups library coverage — no SmallGroups id.