Finite Group Databasebeta

← Prev (#72184354) Next (#72184356) →

C22×C3×C13×C32 #72184355

order4992
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 36864
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C13×C32
multiplicative(ℤ/9992)ˣ, (ℤ/10112)ˣ, (ℤ/14988)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C23×C3×C13
socle, prime radicalC23×C3×C13C16
LCSG ▷ C1
UCSC1 ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4992 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C13×C64, C2×C3×C4×C13×C32, C23×C3×C13×C32, …
maximal normal subgroup ofC22×C3×C13×C64, C2×C3×C4×C13×C32, C23×C3×C13×C32, …
maximal quotient ofC22×C3×C13×C64, C2×C3×C4×C13×C32, C23×C3×C13×C32, …
automorphism group ofC8×C1249, C79×C128
outer automorphism group ofC8×C1249, C79×C128

GAP

Past the SmallGroups library coverage — no SmallGroups id.