Finite Group Databasebeta

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C2×C3×C42×C13×C25 #72207993

order31200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 737280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C42×C13×C25
multiplicative(ℤ/37471)ˣ, (ℤ/39895)ˣ, (ℤ/40015)ˣ, (ℤ/45535)ˣ, (ℤ/46375)ˣ, (ℤ/47571)ˣ, (ℤ/48177)ˣ, (ℤ/50739)ˣ, (ℤ/51207)ˣ, (ℤ/58545)ˣ, (ℤ/58875)ˣ, (ℤ/59625)ˣ, (ℤ/63375)ˣ, (ℤ/63428)ˣ, (ℤ/67652)ˣ, (ℤ/68276)ˣ, (ℤ/74942)ˣ, (ℤ/78500)ˣ, (ℤ/79790)ˣ, (ℤ/80030)ˣ, (ℤ/84500)ˣ, (ℤ/91070)ˣ, (ℤ/92750)ˣ, (ℤ/95142)ˣ, (ℤ/96354)ˣ, (ℤ/101478)ˣ, (ℤ/102414)ˣ, (ℤ/117090)ˣ, (ℤ/117750)ˣ, (ℤ/119250)ˣ, (ℤ/126750)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C5C23×C3×C5×C13
socle, prime radicalC23×C3×C5×C13C22×C5
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

31200 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.