Finite Group Databasebeta

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C25×C3×C4×C5×C8 #72193374

order15360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10736731045232640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C220×C4

Aliases

abelianC25×C3×C4×C5×C8

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C27×C3×C5
socle, prime radicalC27×C3×C5C2×C4
LCSG ▷ C1
UCSC1 ◁ G

816468 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC25×C3×C4×C5×C16, C25×C3×C5×C82, C24×C3×C42×C5×C8, …
maximal normal subgroup ofC25×C3×C4×C5×C16, C25×C3×C5×C82, C24×C3×C42×C5×C8, …
maximal quotient ofC25×C3×C4×C5×C16, C25×C3×C5×C82, C24×C3×C42×C5×C8, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.