Finite Group Databasebeta

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C22×C32×C4×C13×C17 #72208592

order31824
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1769472
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C4×C13×C17
multiplicative(ℤ/38213)ˣ, (ℤ/40313)ˣ, (ℤ/40685)ˣ, (ℤ/46445)ˣ, (ℤ/48513)ˣ, (ℤ/49131)ˣ, (ℤ/51753)ˣ, (ℤ/51831)ˣ, (ℤ/52221)ˣ, (ℤ/59715)ˣ, (ℤ/64684)ˣ, (ℤ/69004)ˣ, (ℤ/69628)ˣ, (ℤ/76426)ˣ, (ℤ/80626)ˣ, (ℤ/81370)ˣ, (ℤ/92890)ˣ, (ℤ/97026)ˣ, (ℤ/98262)ˣ, (ℤ/103506)ˣ, (ℤ/103662)ˣ, (ℤ/104442)ˣ, (ℤ/119430)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C32×C13×C17
socle, prime radicalC23×C32×C13×C17C2
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

31824 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.