Finite Group Databasebeta

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C2×C3×C32×C43 #72187186

order8256
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5376
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C32×C43
multiplicative(ℤ/12387)ˣ, (ℤ/16516)ˣ, (ℤ/24774)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C22×C3×C43
socle, prime radicalC22×C3×C43C16
LCSG ▷ C1
UCSC1 ◁ G

68 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8256 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C43×C64, C3×C4×C32×C43, C22×C3×C32×C43, …
maximal normal subgroup ofC2×C3×C43×C64, C3×C4×C32×C43, C22×C3×C32×C43, …
maximal quotient ofC2×C3×C43×C64, C3×C4×C32×C43, C22×C3×C32×C43, …
automorphism group ofC3×C4129
outer automorphism group ofC3×C4129

GAP

Past the SmallGroups library coverage — no SmallGroups id.