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C2×C9×C23×C29 #26046381

order12006
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3696
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC12006
abelianC2×C9×C23×C29
multiplicative(ℤ/12007)ˣ, (ℤ/24014)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C2×C3×C23×C29
socle, prime radicalC2×C3×C23×C29C3
LCSG ▷ C1
UCSC1 ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12006 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic12006, D24012
Fitting subgroup ofC9×C23×Dic29, C9×C29×Dic23, C9×Dic667, …
maximal subgroup ofC4×C9×C23×C29, C9×C23×Dic29, C9×C29×Dic23, …
maximal normal subgroup ofC4×C9×C23×C29, C9×C23×Dic29, C9×C29×Dic23, …
maximal quotient ofC4×C9×C23×C29, C22×C9×C23×C29
automorphism group ofC12007
outer automorphism group ofC12007

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12006, 1);