Finite Group Databasebeta

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C23×C3×C42×C16 #72185331

order6144
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 17317308137472
homologyAbelianization (H1) = G · Schur multiplier (H2) = C212×C43

Aliases

abelianC23×C3×C42×C16
multiplicative(ℤ/26520)ˣ, (ℤ/28560)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C8C26×C3
socle, prime radicalC26×C3C22×C8
LCSG ▷ C1
UCSC1 ◁ G

155088 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6144 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C42×C32, C23×C3×C4×C8×C16, C22×C3×C43×C16, …
maximal normal subgroup ofC23×C3×C42×C32, C23×C3×C4×C8×C16, C22×C3×C43×C16, …
maximal quotient ofC23×C3×C42×C32, C23×C3×C4×C8×C16, C22×C3×C43×C16, …
automorphism group ofC3×C5×C8×C13×C17, C3×C5×C7×C16×C17
outer automorphism group ofC3×C5×C8×C13×C17, C3×C5×C7×C16×C17

GAP

Past the SmallGroups library coverage — no SmallGroups id.