Finite Group Databasebeta

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C23×C3×C4×C8×C13 #72188652

order9984
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2113929216
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C3×C4×C8×C13
multiplicative(ℤ/35616)ˣ, (ℤ/37560)ˣ, (ℤ/37920)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C25×C3×C13
socle, prime radicalC25×C3×C13C2×C4
LCSG ▷ C1
UCSC1 ◁ G

9276 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9984 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C13×C16, C23×C3×C82×C13, C22×C3×C42×C8×C13, …
maximal normal subgroup ofC23×C3×C4×C13×C16, C23×C3×C82×C13, C22×C3×C42×C8×C13, …
maximal quotient ofC23×C3×C4×C13×C16, C23×C3×C82×C13, C22×C3×C42×C8×C13, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.