Finite Group Databasebeta

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C32×C4×C8×C25 #72186264

order7200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 122880
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C4

Aliases

abelianC32×C4×C8×C25
multiplicative(ℤ/7813)ˣ, (ℤ/15626)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4×C5C22×C32×C5
socle, prime radicalC22×C32×C5C2×C4×C5
LCSG ▷ C1
UCSC1 ◁ G

396 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C4×C16×C25, C32×C82×C25, C2×C32×C4×C8×C25, …
maximal normal subgroup ofC32×C4×C16×C25, C32×C82×C25, C2×C32×C4×C8×C25, …
maximal quotient ofC32×C4×C16×C25, C32×C82×C25, C2×C32×C4×C8×C25, …
automorphism group ofC13×C601
outer automorphism group ofC13×C601

GAP

Past the SmallGroups library coverage — no SmallGroups id.