Finite Group Databasebeta

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C2×C3×C5×C9×C37 #72188658

order9990
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 15552
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC2×C3×C5×C9×C37

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C2×C32×C5×C37
socle, prime radicalC2×C32×C5×C37C3
LCSG ▷ C1
UCSC1 ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9990 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C5×C9×C37, C22×C3×C5×C9×C37, C2×C3×C5×C27×C37, …
maximal normal subgroup ofC3×C4×C5×C9×C37, C22×C3×C5×C9×C37, C2×C3×C5×C27×C37, …
maximal quotient ofC3×C4×C5×C9×C37, C22×C3×C5×C9×C37, C2×C3×C5×C27×C37, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.