Finite Group Databasebeta

← Prev (#72185120) Next (#72185122) →

C2×C4×C11×C67 #72185121

order5896
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C11×C67
multiplicative(ℤ/6187)ˣ, (ℤ/12374)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C11×C67
socle, prime radicalC22×C11×C67C2
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5896 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C8×C11×C67, C42×C11×C67, C22×C4×C11×C67, …
maximal normal subgroup ofC2×C8×C11×C67, C42×C11×C67, C22×C4×C11×C67, …
maximal quotient ofC2×C8×C11×C67, C42×C11×C67, C22×C4×C11×C67, …
automorphism group ofC23×C269
outer automorphism group ofC23×C269

GAP

Past the SmallGroups library coverage — no SmallGroups id.