Finite Group Databasebeta

← Prev (#72189265) Next (#72189267) →

C23×C4×C5×C67 #72189266

order10720
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5677056
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C4×C5×C67
multiplicative(ℤ/23672)ˣ, (ℤ/35508)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C5×C67
socle, prime radicalC24×C5×C67C2
LCSG ▷ C1
UCSC1 ◁ G

472 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C5×C8×C67, C22×C42×C5×C67, C24×C4×C5×C67, …
maximal normal subgroup ofC23×C5×C8×C67, C22×C42×C5×C67, C24×C4×C5×C67, …
maximal quotient ofC23×C5×C8×C67, C22×C42×C5×C67, C24×C4×C5×C67, …
automorphism group ofC8×C11×C269
outer automorphism group ofC8×C11×C269

GAP

Past the SmallGroups library coverage — no SmallGroups id.