Finite Group Databasebeta

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C23×C42×C5×C25 #72193995

order16000
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 132120576000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4×C5

Aliases

abelianC23×C42×C5×C25
multiplicative(ℤ/44440)ˣ, (ℤ/53328)ˣ, (ℤ/60600)ˣ, (ℤ/66000)ˣ, (ℤ/66660)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C5C25×C52
socle, prime radicalC25×C52C22×C5
LCSG ▷ C1
UCSC1 ◁ G

21000 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C5×C8×C25, C22×C43×C5×C25, C24×C42×C5×C25
maximal normal subgroup ofC23×C4×C5×C8×C25, C22×C43×C5×C25, C24×C42×C5×C25
maximal quotient ofC23×C4×C5×C8×C25, C22×C43×C5×C25, C24×C42×C5×C25

GAP

Past the SmallGroups library coverage — no SmallGroups id.