Finite Group Databasebeta

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C25×C3×C8×C16 #72190677

order12288
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 42946924180930560
homologyAbelianization (H1) = G · Schur multiplier (H2) = C220×C8

Aliases

abelianC25×C3×C8×C16

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C8C27×C3
socle, prime radicalC27×C3C4×C8
LCSG ▷ C1
UCSC1 ◁ G

1088246 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC25×C3×C8×C32, C25×C3×C162, C24×C3×C4×C8×C16, …
maximal normal subgroup ofC25×C3×C8×C32, C25×C3×C162, C24×C3×C4×C8×C16, …
maximal quotient ofC25×C3×C8×C32, C25×C3×C162, C24×C3×C4×C8×C16, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.