Finite Group Databasebeta

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C22×C32×C42×C52 #72192573

order14400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3397386240
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4×C5

Aliases

abelianC22×C32×C42×C52
multiplicative(ℤ/22165)ˣ, (ℤ/23485)ˣ, (ℤ/25025)ˣ, (ℤ/26169)ˣ, (ℤ/28365)ˣ, (ℤ/30195)ˣ, (ℤ/30225)ˣ, (ℤ/30256)ˣ, (ℤ/32025)ˣ, (ℤ/32175)ˣ, (ℤ/34892)ˣ, (ℤ/37820)ˣ, (ℤ/40300)ˣ, (ℤ/42700)ˣ, (ℤ/44330)ˣ, (ℤ/46970)ˣ, (ℤ/50050)ˣ, (ℤ/52338)ˣ, (ℤ/54900)ˣ, (ℤ/56730)ˣ, (ℤ/60390)ˣ, (ℤ/60450)ˣ, (ℤ/64050)ˣ, (ℤ/64350)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C24×C32×C52
socle, prime radicalC24×C32×C52C22
LCSG ▷ C1
UCSC1 ◁ G

11952 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×C4×C52×C8, C2×C32×C43×C52, C23×C32×C42×C52
maximal normal subgroup ofC22×C32×C4×C52×C8, C2×C32×C43×C52, C23×C32×C42×C52
maximal quotient ofC22×C32×C4×C52×C8, C2×C32×C43×C52, C23×C32×C42×C52
automorphism group ofC16×C31×C61
outer automorphism group ofC16×C31×C61

GAP

Past the SmallGroups library coverage — no SmallGroups id.