Finite Group Databasebeta

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C23×C7×C11×C13 #72186914

order8008
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 120960
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C7×C11×C13
multiplicative(ℤ/16024)ˣ, (ℤ/24036)ˣ

Subgroups

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

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8008 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C7×C11×C13, C22×C4×C7×C11×C13, C23×C3×C7×C11×C13
maximal normal subgroup ofC24×C7×C11×C13, C22×C4×C7×C11×C13, C23×C3×C7×C11×C13
maximal quotient ofC24×C7×C11×C13, C22×C4×C7×C11×C13, C23×C3×C7×C11×C13

GAP

Past the SmallGroups library coverage — no SmallGroups id.