Finite Group Databasebeta

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C22×C3×C42×C52 #72184239

order4800
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 141557760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4×C5

Aliases

abelianC22×C3×C42×C52
multiplicative(ℤ/10065)ˣ, (ℤ/10725)ˣ, (ℤ/10736)ˣ, (ℤ/12200)ˣ, (ℤ/12400)ˣ, (ℤ/13420)ˣ, (ℤ/14300)ˣ, (ℤ/18300)ˣ, (ℤ/20130)ˣ, (ℤ/21450)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C24×C3×C52
socle, prime radicalC24×C3×C52C22
LCSG ▷ C1
UCSC1 ◁ G

3984 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C52×C8, C2×C3×C43×C52, C23×C3×C42×C52, …
maximal normal subgroup ofC22×C3×C4×C52×C8, C2×C3×C43×C52, C23×C3×C42×C52, …
maximal quotient ofC22×C3×C4×C52×C8, C2×C3×C43×C52, C23×C3×C42×C52, …
automorphism group ofC3×C5×C11×C61, C3×C11×C13×C25, C11×C16×C61, …
outer automorphism group ofC3×C5×C11×C61, C3×C11×C13×C25, C11×C16×C61, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.