Finite Group Databasebeta

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C25×C3×C5×C7 #72183052

order3360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 479969280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210

Aliases

abelianC25×C3×C5×C7
multiplicative(ℤ/11352)ˣ, (ℤ/11928)ˣ, (ℤ/12936)ˣ

Subgroups

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

2992 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C3×C4×C5×C7, C26×C3×C5×C7, C25×C5×C7×C9, …
maximal normal subgroup ofC24×C3×C4×C5×C7, C26×C3×C5×C7, C25×C5×C7×C9, …
maximal quotient ofC24×C3×C4×C5×C7, C26×C3×C5×C7, C25×C5×C7×C9, …
automorphism group ofC3×C8×C11×C43, C3×C7×C8×C71, C3×C8×C11×C49
outer automorphism group ofC3×C8×C11×C43, C3×C7×C8×C71, C3×C8×C11×C49

GAP

Past the SmallGroups library coverage — no SmallGroups id.