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C4×C13×C229 #26045481

order11908
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5472
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC11908
abelianC4×C13×C229
multiplicative(ℤ/11909)ˣ, (ℤ/23818)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C13×C229
socle, prime radicalC2×C13×C229C2
LCSG ▷ C1
UCSC1 ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11908 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic11908, D23816
Fitting subgroup ofC4×C13×C229⋊C3, C4×C13⋊C3×C229, C4×#22581986, …
maximal subgroup ofC3×C4×C13×C229, C4×C13×C229⋊C3, C4×C13⋊C3×C229, …
maximal normal subgroup ofC3×C4×C13×C229, C4×C13×C229⋊C3, C4×C13⋊C3×C229, …
maximal quotient ofC3×C4×C13×C229, Dic3×C13×C229, C8×C13×C229, …
automorphism group ofC11909
outer automorphism group ofC11909

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11908, 1);