Finite Group Databasebeta

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C22×C32×C16×C25 #72192552

order14400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 737280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C16×C25
multiplicative(ℤ/17969)ˣ, (ℤ/23103)ˣ, (ℤ/25221)ˣ, (ℤ/25263)ˣ, (ℤ/33628)ˣ, (ℤ/35938)ˣ, (ℤ/43236)ˣ, (ℤ/46206)ˣ, (ℤ/50442)ˣ, (ℤ/50526)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5×C8C23×C32×C5
socle, prime radicalC23×C32×C5C5×C8
LCSG ▷ C1
UCSC1 ◁ G

882 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 ofC22×C32×C25×C32, C2×C32×C4×C16×C25, C23×C32×C16×C25
maximal normal subgroup ofC22×C32×C25×C32, C2×C32×C4×C16×C25, C23×C32×C16×C25
maximal quotient ofC22×C32×C25×C32, C2×C32×C4×C16×C25, C23×C32×C16×C25
automorphism group ofC7×C17×C151
outer automorphism group ofC7×C17×C151

GAP

Past the SmallGroups library coverage — no SmallGroups id.