Finite Group Databasebeta

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C22×C3×C52×C27 #72186993

order8100
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 933120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3×C5

Aliases

abelianC22×C3×C52×C27
multiplicative(ℤ/8401)ˣ, (ℤ/16802)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C22×C32×C52
socle, prime radicalC22×C32×C52C9
LCSG ▷ C1
UCSC1 ◁ G

560 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8100 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C52×C27, C23×C3×C52×C27, C22×C3×C52×C81, …
maximal normal subgroup ofC2×C3×C4×C52×C27, C23×C3×C52×C27, C22×C3×C52×C81, …
maximal quotient ofC2×C3×C4×C52×C27, C23×C3×C52×C27, C22×C3×C52×C81, …
automorphism group ofC31×C271
outer automorphism group ofC31×C271

GAP

Past the SmallGroups library coverage — no SmallGroups id.