Finite Group Databasebeta

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C25×C3×C5×C23 #72189588

order11040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1759887360
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210

Aliases

abelianC25×C3×C5×C23
multiplicative(ℤ/28952)ˣ, (ℤ/34968)ˣ, (ℤ/36696)ˣ, (ℤ/37224)ˣ, (ℤ/43428)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

2992 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC26×C3×C5×C23, C24×C3×C4×C5×C23
maximal normal subgroup ofC26×C3×C5×C23, C24×C3×C4×C5×C23
maximal quotient ofC26×C3×C5×C23, C24×C3×C4×C5×C23
automorphism group ofC7×C8×C11×C47
outer automorphism group ofC7×C8×C11×C47

GAP

Past the SmallGroups library coverage — no SmallGroups id.