Finite Group Databasebeta

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C23×C32×C4×C7×C11 #72199638

order22176
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 61931520
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC23×C32×C4×C7×C11
multiplicative(ℤ/34615)ˣ, (ℤ/38571)ˣ, (ℤ/40803)ˣ, (ℤ/42021)ˣ, (ℤ/43215)ˣ, (ℤ/43953)ˣ, (ℤ/44505)ˣ, (ℤ/46096)ˣ, (ℤ/48152)ˣ, (ℤ/48615)ˣ, (ℤ/49245)ˣ, (ℤ/50715)ˣ, (ℤ/51428)ˣ, (ℤ/51856)ˣ, (ℤ/52528)ˣ, (ℤ/54404)ˣ, (ℤ/57620)ˣ, (ℤ/58604)ˣ, (ℤ/64820)ˣ, (ℤ/65660)ˣ, (ℤ/66672)ˣ, (ℤ/69230)ˣ, (ℤ/69948)ˣ, (ℤ/72228)ˣ, (ℤ/77142)ˣ, (ℤ/81606)ˣ, (ℤ/83340)ˣ, (ℤ/84042)ˣ, (ℤ/86430)ˣ, (ℤ/87906)ˣ, (ℤ/89010)ˣ, (ℤ/97230)ˣ, (ℤ/98490)ˣ, (ℤ/101430)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C32×C7×C11
socle, prime radicalC24×C32×C7×C11C2
LCSG ▷ C1
UCSC1 ◁ G

2832 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

22176 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.