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C2×C5×C7×C9×C19 #26046072

order11970
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2592
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC11970
abelianC2×C5×C7×C9×C19
multiplicative(ℤ/11971)ˣ, (ℤ/23942)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C2×C3×C5×C7×C19
socle, prime radicalC2×C3×C5×C7×C19C3
LCSG ▷ C1
UCSC1 ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11970 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic11970, D23940
Fitting subgroup ofC5×C7×C9×Dic19, C5×C9×C19×Dic7, C5×C9×Dic133, …
maximal subgroup ofC4×C5×C7×C9×C19, C5×C7×C9×Dic19, C5×C9×C19×Dic7, …
maximal normal subgroup ofC4×C5×C7×C9×C19, C5×C7×C9×Dic19, C5×C9×C19×Dic7, …
maximal quotient ofC4×C5×C7×C9×C19, C22×C5×C7×C9×C19
automorphism group ofC11971
outer automorphism group ofC11971

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 1);