Finite Group Databasebeta

← Prev (#72188295) Next (#72188297) →

C2×C4×C11×C109 #72188296

order9592
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C11×C109
multiplicative(ℤ/11995)ˣ, (ℤ/23990)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C11×C109
socle, prime radicalC22×C11×C109C2
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9592 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C8×C11×C109, C42×C11×C109, C22×C4×C11×C109, …
maximal normal subgroup ofC2×C8×C11×C109, C42×C11×C109, C22×C4×C11×C109, …
maximal quotient ofC2×C8×C11×C109, C42×C11×C109, C22×C4×C11×C109, …
automorphism group ofC5×C2399
outer automorphism group ofC5×C2399

GAP

Past the SmallGroups library coverage — no SmallGroups id.