Finite Group Databasebeta

← Prev (#26044795) Next (#26044797) →

C2×C5×C7×C169 #26044796

order11830
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3744
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC11830
abelianC2×C5×C7×C169
multiplicative(ℤ/11831)ˣ, (ℤ/23662)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC13C2×C5×C7×C13
socle, prime radicalC2×C5×C7×C13C13
LCSG ▷ C1
UCSC1 ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11830 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic11830, D23660
Fitting subgroup ofC5×C7×Dic169, C5×Dic7×C169, C5×Dic1183, …
maximal subgroup ofC4×C5×C7×C169, C5×C7×Dic169, C5×Dic7×C169, …
maximal normal subgroup ofC4×C5×C7×C169, C5×C7×Dic169, C5×Dic7×C169, …
maximal quotient ofC4×C5×C7×C169, C22×C5×C7×C169, C2×C3×C5×C7×C169, …
automorphism group ofC11831
outer automorphism group ofC11831

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11830, 1);