Finite Group Databasebeta

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C2×C3×C4×C11×C27 #72186181

order7128
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 25920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC2×C3×C4×C11×C27
multiplicative(ℤ/7303)ˣ, (ℤ/14606)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C9C22×C32×C11
socle, prime radicalC22×C32×C11C2×C9
LCSG ▷ C1
UCSC1 ◁ G

224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7128 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C8×C11×C27, C3×C42×C11×C27, C22×C3×C4×C11×C27, …
maximal normal subgroup ofC2×C3×C8×C11×C27, C3×C42×C11×C27, C22×C3×C4×C11×C27, …
maximal quotient ofC2×C3×C8×C11×C27, C3×C42×C11×C27, C22×C3×C4×C11×C27, …
automorphism group ofC67×C109
outer automorphism group ofC67×C109

GAP

Past the SmallGroups library coverage — no SmallGroups id.