Finite Group Databasebeta

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C25×C5×C8×C11 #72192247

order14080
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1638295142400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C215

Aliases

abelianC25×C5×C8×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C26×C5×C11
socle, prime radicalC26×C5×C11C4
LCSG ▷ C1
UCSC1 ◁ G

30908 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC25×C5×C11×C16, C24×C4×C5×C8×C11, C26×C5×C8×C11
maximal normal subgroup ofC25×C5×C11×C16, C24×C4×C5×C8×C11, C26×C5×C8×C11
maximal quotient ofC25×C5×C11×C16, C24×C4×C5×C8×C11, C26×C5×C8×C11

GAP

Past the SmallGroups library coverage — no SmallGroups id.