Finite Group Databasebeta

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C23×C32×C4×C7×C13 #72203356

order26208
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 74317824
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC23×C32×C4×C7×C13
multiplicative(ℤ/47859)ˣ, (ℤ/48111)ˣ, (ℤ/50955)ˣ, (ℤ/54008)ˣ, (ℤ/54352)ˣ, (ℤ/56888)ˣ, (ℤ/57435)ˣ, (ℤ/58065)ˣ, (ℤ/58136)ˣ, (ℤ/61208)ˣ, (ℤ/61264)ˣ, (ℤ/61544)ˣ, (ℤ/61936)ˣ, (ℤ/63812)ˣ, (ℤ/64148)ˣ, (ℤ/66248)ˣ, (ℤ/67940)ˣ, (ℤ/76580)ˣ, (ℤ/77420)ˣ, (ℤ/78696)ˣ, (ℤ/78768)ˣ, (ℤ/81012)ˣ, (ℤ/82044)ˣ, (ℤ/82476)ˣ, (ℤ/85332)ˣ, (ℤ/87204)ˣ, (ℤ/91812)ˣ, (ℤ/92316)ˣ, (ℤ/93492)ˣ, (ℤ/95718)ˣ, (ℤ/96222)ˣ, (ℤ/98460)ˣ, (ℤ/99372)ˣ, (ℤ/101910)ˣ, (ℤ/114870)ˣ, (ℤ/116130)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C32×C7×C13
socle, prime radicalC24×C32×C7×C13C2
LCSG ▷ C1
UCSC1 ◁ G

2832 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

26208 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.