Finite Group Databasebeta

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C23×C25×C29 #72185034

order5800
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 94080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C25×C29
multiplicative(ℤ/11608)ˣ, (ℤ/17412)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C23×C5×C29
socle, prime radicalC23×C5×C29C5
LCSG ▷ C1
UCSC1 ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C25×C29, C24×C25×C29, C23×C3×C25×C29, …
maximal normal subgroup ofC22×C4×C25×C29, C24×C25×C29, C23×C3×C25×C29, …
maximal quotient ofC22×C4×C25×C29, C24×C25×C29, C23×C3×C25×C29, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.