Finite Group Databasebeta

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C22×C32×C4×C5×C19 #72191892

order13680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 663552
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C4×C5×C19
multiplicative(ℤ/17381)ˣ, (ℤ/17633)ˣ, (ℤ/19985)ˣ, (ℤ/21297)ˣ, (ℤ/22269)ˣ, (ℤ/22347)ˣ, (ℤ/22671)ˣ, (ℤ/25695)ˣ, (ℤ/28396)ˣ, (ℤ/29692)ˣ, (ℤ/34762)ˣ, (ℤ/35266)ˣ, (ℤ/39970)ˣ, (ℤ/42594)ˣ, (ℤ/44538)ˣ, (ℤ/44694)ˣ, (ℤ/45342)ˣ, (ℤ/51390)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C32×C5×C19
socle, prime radicalC23×C32×C5×C19C2
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C5×C8×C19, C2×C32×C42×C5×C19, C23×C32×C4×C5×C19
maximal normal subgroup ofC22×C32×C5×C8×C19, C2×C32×C42×C5×C19, C23×C32×C4×C5×C19
maximal quotient ofC22×C32×C5×C8×C19, C2×C32×C42×C5×C19, C23×C32×C4×C5×C19
automorphism group ofC7×C13×C191, C7×C11×C229
outer automorphism group ofC7×C13×C191, C7×C11×C229

GAP

Past the SmallGroups library coverage — no SmallGroups id.