Finite Group Databasebeta

← Prev (#72185651) Next (#72185653) →

C2×C4×C5×C163 #72185652

order6520
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5184
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C5×C163
multiplicative(ℤ/7183)ˣ, (ℤ/14366)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C5×C163
socle, prime radicalC22×C5×C163C2
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC42×C5×C163, C2×C5×C8×C163, C22×C4×C5×C163, …
maximal normal subgroup ofC42×C5×C163, C2×C5×C8×C163, C22×C4×C5×C163, …
maximal quotient ofC42×C5×C163, C2×C5×C8×C163, C22×C4×C5×C163, …
automorphism group ofC11×C653
outer automorphism group ofC11×C653

GAP

Past the SmallGroups library coverage — no SmallGroups id.