Finite Group Databasebeta

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C22×C42×C52×C7 #72189692

order11200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 424673280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4×C5

Aliases

abelianC22×C42×C52×C7
multiplicative(ℤ/23925)ˣ, (ℤ/28400)ˣ, (ℤ/31900)ˣ, (ℤ/47850)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C24×C52×C7
socle, prime radicalC24×C52×C7C22
LCSG ▷ C1
UCSC1 ◁ G

3984 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C52×C7×C8, C2×C43×C52×C7, C23×C42×C52×C7
maximal normal subgroup ofC22×C4×C52×C7×C8, C2×C43×C52×C7, C23×C42×C52×C7
maximal quotient ofC22×C4×C52×C7×C8, C2×C43×C52×C7, C23×C42×C52×C7
automorphism group ofC16×C25×C71
outer automorphism group ofC16×C25×C71

GAP

Past the SmallGroups library coverage — no SmallGroups id.