Finite Group Databasebeta

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C23×C4×C5×C79 #72190992

order12640
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6709248
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C4×C5×C79
multiplicative(ℤ/27896)ˣ, (ℤ/41844)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C5×C79
socle, prime radicalC24×C5×C79C2
LCSG ▷ C1
UCSC1 ◁ G

472 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12640 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C5×C8×C79, C22×C42×C5×C79, C24×C4×C5×C79
maximal normal subgroup ofC23×C5×C8×C79, C22×C42×C5×C79, C24×C4×C5×C79
maximal quotient ofC23×C5×C8×C79, C22×C42×C5×C79, C24×C4×C5×C79
automorphism group ofC8×C11×C317
outer automorphism group ofC8×C11×C317

GAP

Past the SmallGroups library coverage — no SmallGroups id.