Finite Group Databasebeta

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C2×C4×C9×C137 #72188571

order9864
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6528
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C9×C137
multiplicative(ℤ/12335)ˣ, (ℤ/14799)ˣ, (ℤ/19732)ˣ, (ℤ/24670)ˣ, (ℤ/29598)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C22×C3×C137
socle, prime radicalC22×C3×C137C2×C3
LCSG ▷ C1
UCSC1 ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9864 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C8×C9×C137, C42×C9×C137, C22×C4×C9×C137, …
maximal normal subgroup ofC2×C8×C9×C137, C42×C9×C137, C22×C4×C9×C137, …
maximal quotient ofC2×C8×C9×C137, C42×C9×C137, C22×C4×C9×C137, …
automorphism group ofC5×C2467
outer automorphism group ofC5×C2467

GAP

Past the SmallGroups library coverage — no SmallGroups id.