Finite Group Databasebeta

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C23×C5×C121 #72184262

order4840
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 73920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C5×C121
multiplicative(ℤ/10648)ˣ, (ℤ/15972)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC11C23×C5×C11
socle, prime radicalC23×C5×C11C11
LCSG ▷ C1
UCSC1 ◁ G

96 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×C121, C24×C5×C121, C23×C3×C5×C121, …
maximal normal subgroup ofC22×C4×C5×C121, C24×C5×C121, C23×C3×C5×C121, …
maximal quotient ofC22×C4×C5×C121, C24×C5×C121, C23×C3×C5×C121, …
automorphism group ofC8×C1331, C3×C4×C1331
outer automorphism group ofC8×C1331, C3×C4×C1331

GAP

Past the SmallGroups library coverage — no SmallGroups id.