Finite Group Databasebeta

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C2×C4×C5×C9×C29 #72189080

order10440
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5376
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C5×C9×C29
multiplicative(ℤ/10679)ˣ, (ℤ/13075)ˣ, (ℤ/21358)ˣ, (ℤ/26150)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C22×C3×C5×C29
socle, prime radicalC22×C3×C5×C29C2×C3
LCSG ▷ C1
UCSC1 ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10440 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C8×C9×C29, C42×C5×C9×C29, C22×C4×C5×C9×C29, …
maximal normal subgroup ofC2×C5×C8×C9×C29, C42×C5×C9×C29, C22×C4×C5×C9×C29, …
maximal quotient ofC2×C5×C8×C9×C29, C42×C5×C9×C29, C22×C4×C5×C9×C29, …
automorphism group ofC59×C181
outer automorphism group ofC59×C181

GAP

Past the SmallGroups library coverage — no SmallGroups id.