Finite Group Databasebeta

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C22×C3×C4×C52×C8 #72188317

order9600
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 188743680
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4×C5

Aliases

abelianC22×C3×C4×C52×C8
multiplicative(ℤ/15785)ˣ, (ℤ/17589)ˣ, (ℤ/19065)ˣ, (ℤ/20008)ˣ, (ℤ/20295)ˣ, (ℤ/20336)ˣ, (ℤ/21472)ˣ, (ℤ/21525)ˣ, (ℤ/23452)ˣ, (ℤ/24800)ˣ, (ℤ/25420)ˣ, (ℤ/28700)ˣ, (ℤ/30012)ˣ, (ℤ/31570)ˣ, (ℤ/35178)ˣ, (ℤ/36900)ˣ, (ℤ/38130)ˣ, (ℤ/40590)ˣ, (ℤ/43050)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C24×C3×C52
socle, prime radicalC24×C3×C52C2×C4
LCSG ▷ C1
UCSC1 ◁ G

6080 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C52×C16, C22×C3×C52×C82, C2×C3×C42×C52×C8, …
maximal normal subgroup ofC22×C3×C4×C52×C16, C22×C3×C52×C82, C2×C3×C42×C52×C8, …
maximal quotient ofC22×C3×C4×C52×C16, C22×C3×C52×C82, C2×C3×C42×C52×C8, …
automorphism group ofC8×C41×C61, C16×C31×C41, C11×C32×C61, …
outer automorphism group ofC8×C41×C61, C16×C31×C41, C11×C32×C61, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.