Finite Group Databasebeta

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C24×C5×C8×C25 #72193989

order16000
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 41287680000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C5

Aliases

abelianC24×C5×C8×C25

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C5C25×C52
socle, prime radicalC25×C52C4×C5
LCSG ▷ C1
UCSC1 ◁ G

13832 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C5×C16×C25, C23×C4×C5×C8×C25, C25×C5×C8×C25
maximal normal subgroup ofC24×C5×C16×C25, C23×C4×C5×C8×C25, C25×C5×C8×C25
maximal quotient ofC24×C5×C16×C25, C23×C4×C5×C8×C25, C25×C5×C8×C25

GAP

Past the SmallGroups library coverage — no SmallGroups id.