Finite Group Databasebeta

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C22×C42×C7×C8 #72183244

order3584
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 14495514624
homologyAbelianization (H1) = G · Schur multiplier (H2) = C27×C43

Aliases

abelianC22×C42×C7×C8
multiplicative(ℤ/13920)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C4C25×C7
socle, prime radicalC25×C7C22×C4
LCSG ▷ C1
UCSC1 ◁ G

13188 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3584 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C42×C7×C16, C22×C4×C7×C82, C2×C43×C7×C8, …
maximal normal subgroup ofC22×C42×C7×C16, C22×C4×C7×C82, C2×C43×C7×C8, …
maximal quotient ofC22×C42×C7×C16, C22×C4×C7×C82, C2×C43×C7×C8, …
automorphism group ofC3×C5×C29×C32
outer automorphism group ofC3×C5×C29×C32

GAP

Past the SmallGroups library coverage — no SmallGroups id.