Finite Group Databasebeta

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C3×C43×C7×C8 #72189308

order10752
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 16911433728
homologyAbelianization (H1) = G · Schur multiplier (H2) = C46

Aliases

abelianC3×C43×C7×C8

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23×C4C24×C3×C7
socle, prime radicalC24×C3×C7C23×C4
LCSG ▷ C1
UCSC1 ◁ G

13320 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10752 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C43×C7×C16, C3×C42×C7×C82, C2×C3×C43×C7×C8, …
maximal normal subgroup ofC3×C43×C7×C16, C3×C42×C7×C82, C2×C3×C43×C7×C8, …
maximal quotient ofC3×C43×C7×C16, C3×C42×C7×C82, C2×C3×C43×C7×C8, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.