Finite Group Databasebeta

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C24×C3×C5×C37 #72187709

order8880
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5806080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C3×C5×C37
multiplicative(ℤ/19624)ˣ, (ℤ/29436)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

536 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8880 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C5×C37, C25×C3×C5×C37, C24×C5×C9×C37, …
maximal normal subgroup ofC23×C3×C4×C5×C37, C25×C3×C5×C37, C24×C5×C9×C37, …
maximal quotient ofC23×C3×C4×C5×C37, C25×C3×C5×C37, C24×C5×C9×C37, …
automorphism group ofC8×C11×C223
outer automorphism group ofC8×C11×C223

GAP

Past the SmallGroups library coverage — no SmallGroups id.