Finite Group Databasebeta

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C24×C32×C4×C52 #72192577

order14400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 237817036800
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C3×C5

Aliases

abelianC24×C32×C4×C52
multiplicative(ℤ/35464)ˣ, (ℤ/35805)ˣ, (ℤ/37576)ˣ, (ℤ/38192)ˣ, (ℤ/43400)ˣ, (ℤ/45384)ˣ, (ℤ/47740)ˣ, (ℤ/48312)ˣ, (ℤ/49104)ˣ, (ℤ/53196)ˣ, (ℤ/55800)ˣ, (ℤ/56364)ˣ, (ℤ/61380)ˣ, (ℤ/65100)ˣ, (ℤ/69300)ˣ, (ℤ/71610)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C32×C52
socle, prime radicalC25×C32×C52C2
LCSG ▷ C1
UCSC1 ◁ G

32688 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C32×C52×C8, C23×C32×C42×C52, C25×C32×C4×C52
maximal normal subgroup ofC24×C32×C52×C8, C23×C32×C42×C52, C25×C32×C4×C52
maximal quotient ofC24×C32×C52×C8, C23×C32×C42×C52, C25×C32×C4×C52

GAP

Past the SmallGroups library coverage — no SmallGroups id.