Finite Group Databasebeta

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C2×C5×C25×C43 #72189286

order10750
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 84000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C5

Aliases

abelianC2×C5×C25×C43

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C2×C52×C43
socle, prime radicalC2×C52×C43C5
LCSG ▷ C1
UCSC1 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10750 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C25×C43, C22×C5×C25×C43, C2×C3×C5×C25×C43
maximal normal subgroup ofC4×C5×C25×C43, C22×C5×C25×C43, C2×C3×C5×C25×C43
maximal quotient ofC4×C5×C25×C43, C22×C5×C25×C43, C2×C3×C5×C25×C43

GAP

Past the SmallGroups library coverage — no SmallGroups id.