Finite Group Databasebeta

← Prev (#72190158) Next (#72190160) →

C2×C4×C7×C11×C19 #72190159

order11704
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C7×C11×C19
multiplicative(ℤ/12151)ˣ, (ℤ/14635)ˣ, (ℤ/24302)ˣ, (ℤ/29270)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C7×C11×C19
socle, prime radicalC22×C7×C11×C19C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11704 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC42×C7×C11×C19, C2×C7×C8×C11×C19, C22×C4×C7×C11×C19
maximal normal subgroup ofC42×C7×C11×C19, C2×C7×C8×C11×C19, C22×C4×C7×C11×C19
maximal quotient ofC42×C7×C11×C19, C2×C7×C8×C11×C19, C22×C4×C7×C11×C19
automorphism group ofC29×C419, C5×C2927
outer automorphism group ofC29×C419, C5×C2927

GAP

Past the SmallGroups library coverage — no SmallGroups id.