Finite Group Databasebeta

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C23×C3×C4×C112 #72190058

order11616
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 567705600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C11

Aliases

abelianC23×C3×C4×C112
multiplicative(ℤ/23115)ˣ, (ℤ/24656)ˣ, (ℤ/30820)ˣ, (ℤ/46230)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C3×C112
socle, prime radicalC24×C3×C112C2
LCSG ▷ C1
UCSC1 ◁ G

3304 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C8×C112, C22×C3×C42×C112, C24×C3×C4×C112
maximal normal subgroup ofC23×C3×C8×C112, C22×C3×C42×C112, C24×C3×C4×C112
maximal quotient ofC23×C3×C8×C112, C22×C3×C42×C112, C24×C3×C4×C112
automorphism group ofC16×C23×C67
outer automorphism group ofC16×C23×C67

GAP

Past the SmallGroups library coverage — no SmallGroups id.