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C2×C3×C52×C7×C8 #72187283

order8400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 92160
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C5

Aliases

abelianC2×C3×C52×C7×C8
multiplicative(ℤ/8651)ˣ, (ℤ/8711)ˣ, (ℤ/17302)ˣ, (ℤ/17422)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C3×C52×C7
socle, prime radicalC22×C3×C52×C7C4
LCSG ▷ C1
UCSC1 ◁ G

352 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C52×C7×C16, C3×C4×C52×C7×C8, C22×C3×C52×C7×C8, …
maximal normal subgroup ofC2×C3×C52×C7×C16, C3×C4×C52×C7×C8, C22×C3×C52×C7×C8, …
maximal quotient ofC2×C3×C52×C7×C16, C3×C4×C52×C7×C8, C22×C3×C52×C7×C8, …
automorphism group ofC41×C211, C31×C281
outer automorphism group ofC41×C211, C31×C281

GAP

Past the SmallGroups library coverage — no SmallGroups id.