Finite Group Databasebeta

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C23×C32×C8×C25 #72192564

order14400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 41287680
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC23×C32×C8×C25
multiplicative(ℤ/33656)ˣ, (ℤ/33824)ˣ, (ℤ/43272)ˣ, (ℤ/43488)ˣ, (ℤ/50484)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C5C24×C32×C5
socle, prime radicalC24×C32×C5C4×C5
LCSG ▷ C1
UCSC1 ◁ G

3042 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C32×C16×C25, C22×C32×C4×C8×C25, C24×C32×C8×C25
maximal normal subgroup ofC23×C32×C16×C25, C22×C32×C4×C8×C25, C24×C32×C8×C25
maximal quotient ofC23×C32×C16×C25, C22×C32×C4×C8×C25, C24×C32×C8×C25

GAP

Past the SmallGroups library coverage — no SmallGroups id.