Finite Group Databasebeta

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C22×C4×C5×C82 #72184476

order5120
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 77309411328
homologyAbelianization (H1) = G · Schur multiplier (H2) = C27×C42×C8

Aliases

abelianC22×C4×C5×C82
multiplicative(ℤ/19680)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C42C25×C5
socle, prime radicalC25×C5C2×C42
LCSG ▷ C1
UCSC1 ◁ G

25194 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C5×C8×C16, C22×C5×C83, C2×C42×C5×C82, …
maximal normal subgroup ofC22×C4×C5×C8×C16, C22×C5×C83, C2×C42×C5×C82, …
maximal quotient ofC22×C4×C5×C8×C16, C22×C5×C83, C2×C42×C5×C82, …
automorphism group ofC3×C5×C32×C41
outer automorphism group ofC3×C5×C32×C41

GAP

Past the SmallGroups library coverage — no SmallGroups id.