Finite Group Databasebeta

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C22×C3×C4×C8×C27 #72189016

order10368
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 63700992
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4

Aliases

abelianC22×C3×C4×C8×C27
multiplicative(ℤ/24416)ˣ, (ℤ/31392)ˣ, (ℤ/33696)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4×C9C24×C32
socle, prime radicalC24×C32C2×C4×C9
LCSG ▷ C1
UCSC1 ◁ G

5320 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 ofC22×C3×C4×C16×C27, C22×C3×C82×C27, C2×C3×C42×C8×C27, …
maximal normal subgroup ofC22×C3×C4×C16×C27, C22×C3×C82×C27, C2×C3×C42×C8×C27, …
maximal quotient ofC22×C3×C4×C16×C27, C22×C3×C82×C27, C2×C3×C42×C8×C27, …
automorphism group ofC7×C32×C109, C9×C32×C109
outer automorphism group ofC7×C32×C109, C9×C32×C109

GAP

Past the SmallGroups library coverage — no SmallGroups id.