Finite Group Databasebeta

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C22×C7×C11×C27 #72187231

order8316
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6480
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C7×C11×C27
multiplicative(ℤ/8717)ˣ, (ℤ/12477)ˣ, (ℤ/16636)ˣ, (ℤ/17434)ˣ, (ℤ/24954)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C22×C3×C7×C11
socle, prime radicalC22×C3×C7×C11C9
LCSG ▷ C1
UCSC1 ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8316 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C7×C11×C27, C23×C7×C11×C27, C22×C7×C11×C81, …
maximal normal subgroup ofC2×C4×C7×C11×C27, C23×C7×C11×C27, C22×C7×C11×C81, …
maximal quotient ofC2×C4×C7×C11×C27, C23×C7×C11×C27, C22×C7×C11×C81, …
automorphism group ofC23×C379, C3×C4159
outer automorphism group ofC23×C379, C3×C4159

GAP

Past the SmallGroups library coverage — no SmallGroups id.