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C22×C32×C4×C5×C7 #72184404

order5040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 221184
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C4×C5×C7
multiplicative(ℤ/6149)ˣ, (ℤ/6293)ˣ, (ℤ/6461)ˣ, (ℤ/6665)ˣ, (ℤ/7007)ˣ, (ℤ/7385)ˣ, (ℤ/7525)ˣ, (ℤ/7595)ˣ, (ℤ/7869)ˣ, (ℤ/8091)ˣ, (ℤ/8229)ˣ, (ℤ/8307)ˣ, (ℤ/8841)ˣ, (ℤ/8967)ˣ, (ℤ/9495)ˣ, (ℤ/9675)ˣ, (ℤ/10492)ˣ, (ℤ/10972)ˣ, (ℤ/11025)ˣ, (ℤ/11788)ˣ, (ℤ/11956)ˣ, (ℤ/12298)ˣ, (ℤ/12586)ˣ, (ℤ/12922)ˣ, (ℤ/13330)ˣ, (ℤ/14014)ˣ, (ℤ/14770)ˣ, (ℤ/15050)ˣ, (ℤ/15156)ˣ, (ℤ/15190)ˣ, (ℤ/15738)ˣ, (ℤ/16182)ˣ, (ℤ/16458)ˣ, (ℤ/16614)ˣ, (ℤ/17682)ˣ, (ℤ/17934)ˣ, (ℤ/18990)ˣ, (ℤ/19350)ˣ, (ℤ/22050)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C32×C5×C7
socle, prime radicalC23×C32×C5×C7C2
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C5×C7×C8, C2×C32×C42×C5×C7, C23×C32×C4×C5×C7, …
maximal normal subgroup ofC22×C32×C5×C7×C8, C2×C32×C42×C5×C7, C23×C32×C4×C5×C7, …
maximal quotient ofC22×C32×C5×C7×C8, C2×C32×C42×C5×C7, C23×C32×C4×C5×C7, …
automorphism group ofC11×C13×C43, C7×C29×C31, C7×C13×C71, …
outer automorphism group ofC11×C13×C43, C7×C29×C31, C7×C13×C71, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.