Finite Group Databasebeta

← Prev (#72188473) Next (#72188475) →

C4×C5×C8×C61 #72188474

order9760
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 30720
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C5×C8×C61
multiplicative(ℤ/12205)ˣ, (ℤ/24410)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C22×C5×C61
socle, prime radicalC22×C5×C61C2×C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9760 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C16×C61, C5×C82×C61, C2×C4×C5×C8×C61, …
maximal normal subgroup ofC4×C5×C16×C61, C5×C82×C61, C2×C4×C5×C8×C61, …
maximal quotient ofC4×C5×C16×C61, C5×C82×C61, C2×C4×C5×C8×C61, …
automorphism group ofC5×C2441
outer automorphism group ofC5×C2441

GAP

Past the SmallGroups library coverage — no SmallGroups id.