Finite Group Databasebeta

← Prev (#72187808) Next (#72187810) →

C2×C4×C23×C49 #72187809

order9016
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7392
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C23×C49
multiplicative(ℤ/9259)ˣ, (ℤ/18518)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C7C22×C7×C23
socle, prime radicalC22×C7×C23C2×C7
LCSG ▷ C1
UCSC1 ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9016 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C8×C23×C49, C42×C23×C49, C22×C4×C23×C49, …
maximal normal subgroup ofC2×C8×C23×C49, C42×C23×C49, C22×C4×C23×C49, …
maximal quotient ofC2×C8×C23×C49, C42×C23×C49, C22×C4×C23×C49, …
automorphism group ofC47×C197
outer automorphism group ofC47×C197

GAP

Past the SmallGroups library coverage — no SmallGroups id.