Finite Group Databasebeta

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C23×C4×C7×C16 #72183239

order3584
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1056964608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C4×C7×C16
multiplicative(ℤ/11832)ˣ, (ℤ/13560)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C25×C7
socle, prime radicalC25×C7C2×C8
LCSG ▷ C1
UCSC1 ◁ G

6276 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3584 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C7×C32, C23×C7×C8×C16, C22×C42×C7×C16, …
maximal normal subgroup ofC23×C4×C7×C32, C23×C7×C8×C16, C22×C42×C7×C16, …
maximal quotient ofC23×C4×C7×C32, C23×C7×C8×C16, C22×C42×C7×C16, …
automorphism group ofC3×C8×C17×C29, C3×C5×C8×C113
outer automorphism group ofC3×C8×C17×C29, C3×C5×C8×C113

GAP

Past the SmallGroups library coverage — no SmallGroups id.