Finite Group Databasebeta

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C22×C5×C7×C25 #72183161

order3500
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 72000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C5

Aliases

abelianC22×C5×C7×C25

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C22×C52×C7
socle, prime radicalC22×C52×C7C5
LCSG ▷ C1
UCSC1 ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3500 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C5×C7×C25, C23×C5×C7×C25, C22×C3×C5×C7×C25, …
maximal normal subgroup ofC2×C4×C5×C7×C25, C23×C5×C7×C25, C22×C3×C5×C7×C25, …
maximal quotient ofC2×C4×C5×C7×C25, C23×C5×C7×C25, C22×C3×C5×C7×C25, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.