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C3×C31×C64 #72185154

order5952
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C23×C3×C5×C16 (order 1920) · Inn(G) = C1 · Out(G) = C23×C3×C5×C16
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC5952
abelianC3×C31×C64
multiplicative(ℤ/5953)ˣ, (ℤ/11906)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC32C2×C3×C31
socle, prime radicalC2×C3×C31C32
LCSG ▷ C1
UCSC1 ◁ G

28 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5952 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C31×C128, C2×C3×C31×C64, C9×C31×C64, …
maximal normal subgroup ofC3×C31×C128, C2×C3×C31×C64, C9×C31×C64, …
maximal quotient ofC3×C31×C128, C2×C3×C31×C64, C9×C31×C64, …
automorphism group ofC5953, C2×C5953
outer automorphism group ofC5953, C2×C5953

GAP

Past the SmallGroups library coverage — no SmallGroups id.