Finite Group Databasebeta

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C4×C5×C17×C25 #72187371

order8500
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 64000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C5

Aliases

abelianC4×C5×C17×C25

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C5C2×C52×C17
socle, prime radicalC2×C52×C17C2×C5
LCSG ▷ C1
UCSC1 ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8500 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C8×C17×C25, C2×C4×C5×C17×C25, C3×C4×C5×C17×C25
maximal normal subgroup ofC5×C8×C17×C25, C2×C4×C5×C17×C25, C3×C4×C5×C17×C25
maximal quotient ofC5×C8×C17×C25, C2×C4×C5×C17×C25, C3×C4×C5×C17×C25

GAP

Past the SmallGroups library coverage — no SmallGroups id.