Finite Group Databasebeta

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C23×C52×C7×C8 #72189688

order11200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 123863040
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C5

Aliases

abelianC23×C52×C7×C8
multiplicative(ℤ/23288)ˣ, (ℤ/24728)ˣ, (ℤ/24992)ˣ, (ℤ/34932)ˣ, (ℤ/37092)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C24×C52×C7
socle, prime radicalC24×C52×C7C4
LCSG ▷ C1
UCSC1 ◁ G

2704 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 ofC23×C52×C7×C16, C22×C4×C52×C7×C8, C24×C52×C7×C8
maximal normal subgroup ofC23×C52×C7×C16, C22×C4×C52×C7×C8, C24×C52×C7×C8
maximal quotient ofC23×C52×C7×C16, C22×C4×C52×C7×C8, C24×C52×C7×C8
automorphism group ofC8×C41×C71, C8×C11×C281, C11×C32×C71
outer automorphism group ofC8×C41×C71, C8×C11×C281, C11×C32×C71

GAP

Past the SmallGroups library coverage — no SmallGroups id.