Finite Group Databasebeta

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C23×C3×C4×C32 #72182813

order3072
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 704643072
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C3×C4×C32
multiplicative(ℤ/11640)ˣ, (ℤ/13440)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C16C25×C3
socle, prime radicalC25×C3C2×C16
LCSG ▷ C1
UCSC1 ◁ G

7914 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C64, C23×C3×C8×C32, C22×C3×C42×C32, …
maximal normal subgroup ofC23×C3×C4×C64, C23×C3×C8×C32, C22×C3×C42×C32, …
maximal quotient ofC23×C3×C4×C64, C23×C3×C8×C32, C22×C3×C42×C32, …
automorphism group ofC3×C5×C8×C97, C3×C5×C7×C128
outer automorphism group ofC3×C5×C8×C97, C3×C5×C7×C128

GAP

Past the SmallGroups library coverage — no SmallGroups id.