Finite Group Databasebeta

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C22×C3×C27×C37 #72190399

order11988
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 69984
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C3×C27×C37
multiplicative(ℤ/13993)ˣ, (ℤ/17991)ˣ, (ℤ/18063)ˣ, (ℤ/27986)ˣ, (ℤ/35982)ˣ, (ℤ/36126)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C22×C32×C37
socle, prime radicalC22×C32×C37C9
LCSG ▷ C1
UCSC1 ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11988 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C27×C37, C23×C3×C27×C37
maximal normal subgroup ofC2×C3×C4×C27×C37, C23×C3×C27×C37
maximal quotient ofC2×C3×C4×C27×C37, C23×C3×C27×C37
automorphism group ofC7×C1999
outer automorphism group ofC7×C1999

GAP

Past the SmallGroups library coverage — no SmallGroups id.