Finite Group Databasebeta

← Prev (#72190835) Next (#72190837) →

C22×C4×C11×C71 #72190836

order12496
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 134400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C11×C71

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C11×C71
socle, prime radicalC23×C11×C71C2
LCSG ▷ C1
UCSC1 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12496 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C8×C11×C71, C2×C42×C11×C71, C23×C4×C11×C71
maximal normal subgroup ofC22×C8×C11×C71, C2×C42×C11×C71, C23×C4×C11×C71
maximal quotient ofC22×C8×C11×C71, C2×C42×C11×C71, C23×C4×C11×C71

GAP

Past the SmallGroups library coverage — no SmallGroups id.