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C22×C3×C4×C52×C13 #72193633

order15600
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2211840
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C5

Aliases

abelianC22×C3×C4×C52×C13
multiplicative(ℤ/18073)ˣ, (ℤ/18733)ˣ, (ℤ/20305)ˣ, (ℤ/21725)ˣ, (ℤ/22925)ˣ, (ℤ/23973)ˣ, (ℤ/29475)ˣ, (ℤ/31964)ˣ, (ℤ/36146)ˣ, (ℤ/37466)ˣ, (ℤ/40610)ˣ, (ℤ/43450)ˣ, (ℤ/45850)ˣ, (ℤ/47946)ˣ, (ℤ/58950)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C52×C13
socle, prime radicalC23×C3×C52×C13C2
LCSG ▷ C1
UCSC1 ◁ G

864 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C52×C8×C13, C2×C3×C42×C52×C13, C23×C3×C4×C52×C13
maximal normal subgroup ofC22×C3×C52×C8×C13, C2×C3×C42×C52×C13, C23×C3×C4×C52×C13
maximal quotient ofC22×C3×C52×C8×C13, C2×C3×C42×C52×C13, C23×C3×C4×C52×C13
automorphism group ofC11×C31×C53
outer automorphism group ofC11×C31×C53

GAP

Past the SmallGroups library coverage — no SmallGroups id.