Finite Group Databasebeta

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C22×C4×C5×C169 #72191769

order13520
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 119808
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C5×C169
multiplicative(ℤ/22341)ˣ, (ℤ/29788)ˣ, (ℤ/44682)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C13C23×C5×C13
socle, prime radicalC23×C5×C13C2×C13
LCSG ▷ C1
UCSC1 ◁ G

162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C8×C169, C2×C42×C5×C169, C23×C4×C5×C169
maximal normal subgroup ofC22×C5×C8×C169, C2×C42×C5×C169, C23×C4×C5×C169
maximal quotient ofC22×C5×C8×C169, C2×C42×C5×C169, C23×C4×C5×C169

GAP

Past the SmallGroups library coverage — no SmallGroups id.