Finite Group Databasebeta

← Prev (#72189970) Next (#72189972) →

C22×C43×C5×C9 #72189971

order11520
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 50734301184
homologyAbelianization (H1) = G · Schur multiplier (H2) = C27×C43

Aliases

abelianC22×C43×C5×C9
multiplicative(ℤ/32560)ˣ, (ℤ/43440)ˣ, (ℤ/44400)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23×C3C25×C3×C5
socle, prime radicalC25×C3×C5C23×C3
LCSG ▷ C1
UCSC1 ◁ G

24282 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C42×C5×C8×C9, C2×C44×C5×C9, C23×C43×C5×C9
maximal normal subgroup ofC22×C42×C5×C8×C9, C2×C44×C5×C9, C23×C43×C5×C9
maximal quotient ofC22×C42×C5×C8×C9, C2×C44×C5×C9, C23×C43×C5×C9
automorphism group ofC5×C11×C16×C37
outer automorphism group ofC5×C11×C16×C37

GAP

Past the SmallGroups library coverage — no SmallGroups id.