Finite Group Databasebeta

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C23×C32×C4×C5×C13 #72196491

order18720
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 49545216
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC23×C32×C4×C5×C13
multiplicative(ℤ/30415)ˣ, (ℤ/33891)ˣ, (ℤ/34503)ˣ, (ℤ/35763)ˣ, (ℤ/36267)ˣ, (ℤ/36729)ˣ, (ℤ/36735)ˣ, (ℤ/38552)ˣ, (ℤ/38936)ˣ, (ℤ/39039)ˣ, (ℤ/39105)ˣ, (ℤ/39184)ˣ, (ℤ/41265)ˣ, (ℤ/41475)ˣ, (ℤ/41912)ˣ, (ℤ/45188)ˣ, (ℤ/46004)ˣ, (ℤ/47684)ˣ, (ℤ/48356)ˣ, (ℤ/48980)ˣ, (ℤ/52052)ˣ, (ℤ/55300)ˣ, (ℤ/57828)ˣ, (ℤ/58404)ˣ, (ℤ/59148)ˣ, (ℤ/60830)ˣ, (ℤ/61308)ˣ, (ℤ/62172)ˣ, (ℤ/62868)ˣ, (ℤ/66924)ˣ, (ℤ/67782)ˣ, (ℤ/69006)ˣ, (ℤ/71100)ˣ, (ℤ/71526)ˣ, (ℤ/72534)ˣ, (ℤ/73458)ˣ, (ℤ/73470)ˣ, (ℤ/78078)ˣ, (ℤ/78210)ˣ, (ℤ/82530)ˣ, (ℤ/82950)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C32×C5×C13
socle, prime radicalC24×C32×C5×C13C2
LCSG ▷ C1
UCSC1 ◁ G

2832 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

18720 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.