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C22×C32×C4×C5×C13 #72188143

order9360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 442368
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C4×C5×C13
multiplicative(ℤ/11297)ˣ, (ℤ/11501)ˣ, (ℤ/11921)ˣ, (ℤ/12089)ˣ, (ℤ/12245)ˣ, (ℤ/13013)ˣ, (ℤ/13825)ˣ, (ℤ/14457)ˣ, (ℤ/14601)ˣ, (ℤ/14787)ˣ, (ℤ/15327)ˣ, (ℤ/15543)ˣ, (ℤ/15717)ˣ, (ℤ/16731)ˣ, (ℤ/17775)ˣ, (ℤ/19276)ˣ, (ℤ/19468)ˣ, (ℤ/20956)ˣ, (ℤ/22594)ˣ, (ℤ/23002)ˣ, (ℤ/23842)ˣ, (ℤ/24178)ˣ, (ℤ/24490)ˣ, (ℤ/26026)ˣ, (ℤ/27650)ˣ, (ℤ/28914)ˣ, (ℤ/29202)ˣ, (ℤ/29574)ˣ, (ℤ/30654)ˣ, (ℤ/31086)ˣ, (ℤ/31434)ˣ, (ℤ/33462)ˣ, (ℤ/35550)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C32×C5×C13
socle, prime radicalC23×C32×C5×C13C2
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C5×C8×C13, C2×C32×C42×C5×C13, C23×C32×C4×C5×C13, …
maximal normal subgroup ofC22×C32×C5×C8×C13, C2×C32×C42×C5×C13, C23×C32×C4×C5×C13, …
maximal quotient ofC22×C32×C5×C8×C13, C2×C32×C42×C5×C13, C23×C32×C4×C5×C13, …
automorphism group ofC7×C31×C53, C7×C11×C157
outer automorphism group ofC7×C31×C53, C7×C11×C157

GAP

Past the SmallGroups library coverage — no SmallGroups id.