Finite Group Databasebeta

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C2×C3×C42×C7×C16 #72189303

order10752
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 150994944
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C43

Aliases

abelianC2×C3×C42×C7×C16
multiplicative(ℤ/17255)ˣ, (ℤ/19227)ˣ, (ℤ/22035)ˣ, (ℤ/22185)ˣ, (ℤ/23504)ˣ, (ℤ/24128)ˣ, (ℤ/25636)ˣ, (ℤ/26960)ˣ, (ℤ/29380)ˣ, (ℤ/34510)ˣ, (ℤ/38454)ˣ, (ℤ/44070)ˣ, (ℤ/44370)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C8C24×C3×C7
socle, prime radicalC24×C3×C7C22×C8
LCSG ▷ C1
UCSC1 ◁ G

5640 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10752 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C42×C7×C32, C2×C3×C4×C7×C8×C16, C3×C43×C7×C16, …
maximal normal subgroup ofC2×C3×C42×C7×C32, C2×C3×C4×C7×C8×C16, C3×C43×C7×C16, …
maximal quotient ofC2×C3×C42×C7×C32, C2×C3×C4×C7×C8×C16, C3×C43×C7×C16, …
automorphism group ofC13×C16×C113, C13×C29×C64, C5×C16×C337
outer automorphism group ofC13×C16×C113, C13×C29×C64, C5×C16×C337

GAP

Past the SmallGroups library coverage — no SmallGroups id.