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C2×C3×C4×C5×C8×C17 #72194249

order16320
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 262144
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C4×C5×C8×C17
multiplicative(ℤ/19591)ˣ, (ℤ/21115)ˣ, (ℤ/21235)ˣ, (ℤ/22495)ˣ, (ℤ/23975)ˣ, (ℤ/25071)ˣ, (ℤ/30675)ˣ, (ℤ/30825)ˣ, (ℤ/32672)ˣ, (ℤ/33428)ˣ, (ℤ/39182)ˣ, (ℤ/40900)ˣ, (ℤ/42230)ˣ, (ℤ/42470)ˣ, (ℤ/44990)ˣ, (ℤ/47950)ˣ, (ℤ/50142)ˣ, (ℤ/61350)ˣ, (ℤ/61650)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C23×C3×C5×C17
socle, prime radicalC23×C3×C5×C17C2×C4
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C5×C16×C17, C2×C3×C5×C82×C17, C3×C42×C5×C8×C17, …
maximal normal subgroup ofC2×C3×C4×C5×C16×C17, C2×C3×C5×C82×C17, C3×C42×C5×C8×C17, …
maximal quotient ofC2×C3×C4×C5×C16×C17, C2×C3×C5×C82×C17, C3×C42×C5×C8×C17, …
automorphism group ofC11×C13×C137
outer automorphism group ofC11×C13×C137

GAP

Past the SmallGroups library coverage — no SmallGroups id.