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C2×C3×C4×C373 #72187751

order8952
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5952
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C373
multiplicative(ℤ/10451)ˣ, (ℤ/11195)ˣ, (ℤ/13437)ˣ, (ℤ/20902)ˣ, (ℤ/22390)ˣ, (ℤ/26874)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C373
socle, prime radicalC22×C3×C373C2
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8952 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C8×C373, C3×C42×C373, C22×C3×C4×C373, …
maximal normal subgroup ofC2×C3×C8×C373, C3×C42×C373, C22×C3×C4×C373, …
maximal quotient ofC2×C3×C8×C373, C3×C42×C373, C22×C3×C4×C373, …
automorphism group ofC7×C1493, C5×C2239
outer automorphism group ofC7×C1493, C5×C2239

GAP

Past the SmallGroups library coverage — no SmallGroups id.