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C2×C3×C5×C16×C23 #72189583

order11040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5632
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C5×C16×C23
multiplicative(ℤ/11327)ˣ, (ℤ/11747)ˣ, (ℤ/16563)ˣ, (ℤ/22084)ˣ, (ℤ/22654)ˣ, (ℤ/23494)ˣ, (ℤ/33126)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C3×C5×C23
socle, prime radicalC22×C3×C5×C23C8
LCSG ▷ C1
UCSC1 ◁ G

112 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 ofC2×C3×C5×C23×C32, C3×C4×C5×C16×C23, C22×C3×C5×C16×C23
maximal normal subgroup ofC2×C3×C5×C23×C32, C3×C4×C5×C16×C23, C22×C3×C5×C16×C23
maximal quotient ofC2×C3×C5×C23×C32, C3×C4×C5×C16×C23, C22×C3×C5×C16×C23
automorphism group ofC47×C241, C17×C691
outer automorphism group ofC47×C241, C17×C691

GAP

Past the SmallGroups library coverage — no SmallGroups id.