Finite Group Databasebeta

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C25×C33×C7 #72185239

order6048
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 673876869120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C33

Aliases

abelianC25×C33×C7
multiplicative(ℤ/21672)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

20944 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6048 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C33×C4×C7, C26×C33×C7, C25×C32×C7×C9, …
maximal normal subgroup ofC24×C33×C4×C7, C26×C33×C7, C25×C32×C7×C9, …
maximal quotient ofC24×C33×C4×C7, C26×C33×C7, C25×C32×C7×C9, …
automorphism group ofC7×C8×C9×C43
outer automorphism group ofC7×C8×C9×C43

GAP

Past the SmallGroups library coverage — no SmallGroups id.