Finite Group Databasebeta

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C2×C3×C4×C16×C27 #72188996

order10368
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1327104
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4

Aliases

abelianC2×C3×C4×C16×C27
multiplicative(ℤ/12971)ˣ, (ℤ/15155)ˣ, (ℤ/16677)ˣ, (ℤ/16887)ˣ, (ℤ/17901)ˣ, (ℤ/19485)ˣ, (ℤ/22516)ˣ, (ℤ/25942)ˣ, (ℤ/30310)ˣ, (ℤ/33354)ˣ, (ℤ/33774)ˣ, (ℤ/35802)ˣ, (ℤ/38970)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8×C9C23×C32
socle, prime radicalC23×C32C2×C8×C9
LCSG ▷ C1
UCSC1 ◁ G

1512 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C27×C32, C2×C3×C8×C16×C27, C3×C42×C16×C27, …
maximal normal subgroup ofC2×C3×C4×C27×C32, C2×C3×C8×C16×C27, C3×C42×C16×C27, …
maximal quotient ofC2×C3×C4×C27×C32, C2×C3×C8×C16×C27, C3×C42×C16×C27, …
automorphism group ofC7×C17×C109, C5×C7×C433, C13×C17×C81
outer automorphism group ofC7×C17×C109, C5×C7×C433, C13×C17×C81

GAP

Past the SmallGroups library coverage — no SmallGroups id.