Finite Group Databasebeta

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C23×C7×C8×C25 #72189687

order11200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5160960
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C7×C8×C25

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C5C24×C5×C7
socle, prime radicalC24×C5×C7C4×C5
LCSG ▷ C1
UCSC1 ◁ G

1014 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C7×C16×C25, C22×C4×C7×C8×C25, C24×C7×C8×C25
maximal normal subgroup ofC23×C7×C16×C25, C22×C4×C7×C8×C25, C24×C7×C8×C25
maximal quotient ofC23×C7×C16×C25, C22×C4×C7×C8×C25, C24×C7×C8×C25

GAP

Past the SmallGroups library coverage — no SmallGroups id.