Finite Group Databasebeta

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C2×C4×C52×C8×C9 #72192559

order14400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5898240
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4×C5

Aliases

abelianC2×C4×C52×C8×C9
multiplicative(ℤ/16687)ˣ, (ℤ/19475)ˣ, (ℤ/20075)ˣ, (ℤ/22263)ˣ, (ℤ/27675)ˣ, (ℤ/29684)ˣ, (ℤ/33374)ˣ, (ℤ/38950)ˣ, (ℤ/40150)ˣ, (ℤ/44526)ˣ, (ℤ/55350)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C4C23×C3×C52
socle, prime radicalC23×C3×C52C2×C3×C4
LCSG ▷ C1
UCSC1 ◁ G

1944 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C52×C9×C16, C2×C52×C82×C9, C42×C52×C8×C9, …
maximal normal subgroup ofC2×C4×C52×C9×C16, C2×C52×C82×C9, C42×C52×C8×C9, …
maximal quotient ofC2×C4×C52×C9×C16, C2×C52×C82×C9, C42×C52×C8×C9, …
automorphism group ofC11×C37×C41, C25×C27×C41
outer automorphism group ofC11×C37×C41, C25×C27×C41

GAP

Past the SmallGroups library coverage — no SmallGroups id.