Finite Group Databasebeta

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C24×C3×C4×C27 #72184559

order5184
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3344302080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C3

Aliases

abelianC24×C3×C4×C27
multiplicative(ℤ/18312)ˣ, (ℤ/22680)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C9C25×C32
socle, prime radicalC25×C32C2×C9
LCSG ▷ C1
UCSC1 ◁ G

9534 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C3×C8×C27, C23×C3×C42×C27, C25×C3×C4×C27, …
maximal normal subgroup ofC24×C3×C8×C27, C23×C3×C42×C27, C25×C3×C4×C27, …
maximal quotient ofC24×C3×C8×C27, C23×C3×C42×C27, C25×C3×C4×C27, …
automorphism group ofC3×C7×C8×C109, C5×C7×C8×C81
outer automorphism group ofC3×C7×C8×C109, C5×C7×C8×C81

GAP

Past the SmallGroups library coverage — no SmallGroups id.