Finite Group Databasebeta

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C22×C3×C4×C5×C7×C17 #72205506

order28560
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 147456
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C5×C7×C17
multiplicative(ℤ/32857)ˣ, (ℤ/34177)ˣ, (ℤ/36565)ˣ, (ℤ/37045)ˣ, (ℤ/41825)ˣ, (ℤ/43737)ˣ, (ℤ/47157)ˣ, (ℤ/50001)ˣ, (ℤ/53565)ˣ, (ℤ/53775)ˣ, (ℤ/57136)ˣ, (ℤ/58316)ˣ, (ℤ/62876)ˣ, (ℤ/65714)ˣ, (ℤ/66668)ˣ, (ℤ/68354)ˣ, (ℤ/71420)ˣ, (ℤ/73130)ˣ, (ℤ/74090)ˣ, (ℤ/83650)ˣ, (ℤ/85716)ˣ, (ℤ/87474)ˣ, (ℤ/94314)ˣ, (ℤ/100002)ˣ, (ℤ/107130)ˣ, (ℤ/107550)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C5×C7×C17
socle, prime radicalC23×C3×C5×C7×C17C2
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

28560 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.