Finite Group Databasebeta

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C23×C33×C7×C8 #72190484

order12096
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2898395136
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C33

Aliases

abelianC23×C33×C7×C8

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C24×C33×C7
socle, prime radicalC24×C33×C7C4
LCSG ▷ C1
UCSC1 ◁ G

9464 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C33×C7×C16, C22×C33×C4×C7×C8, C24×C33×C7×C8
maximal normal subgroup ofC23×C33×C7×C16, C22×C33×C4×C7×C8, C24×C33×C7×C8
maximal quotient ofC23×C33×C7×C16, C22×C33×C4×C7×C8, C24×C33×C7×C8

GAP

Past the SmallGroups library coverage — no SmallGroups id.