Finite Group Databasebeta

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C23×C5×C112 #72184263

order4840
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8870400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C11

Aliases

abelianC23×C5×C112
multiplicative(ℤ/8349)ˣ, (ℤ/11132)ˣ, (ℤ/16698)ˣ

Subgroups

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

448 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C5×C112, C24×C5×C112, C23×C3×C5×C112, …
maximal normal subgroup ofC22×C4×C5×C112, C24×C5×C112, C23×C3×C5×C112, …
maximal quotient ofC22×C4×C5×C112, C24×C5×C112, C23×C3×C5×C112, …
automorphism group ofC3×C23×C121, C4×C23×C121
outer automorphism group ofC3×C23×C121, C4×C23×C121

GAP

Past the SmallGroups library coverage — no SmallGroups id.