Finite Group Databasebeta

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C22×C4×C5×C9×C13 #72188142

order9360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 55296
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C5×C9×C13
multiplicative(ℤ/11077)ˣ, (ℤ/12445)ˣ, (ℤ/14541)ˣ, (ℤ/15741)ˣ, (ℤ/17565)ˣ, (ℤ/17685)ˣ, (ℤ/18728)ˣ, (ℤ/18736)ˣ, (ℤ/19388)ˣ, (ℤ/22154)ˣ, (ℤ/23420)ˣ, (ℤ/24890)ˣ, (ℤ/28092)ˣ, (ℤ/29082)ˣ, (ℤ/31482)ˣ, (ℤ/35130)ˣ, (ℤ/35370)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C23×C3×C5×C13
socle, prime radicalC23×C3×C5×C13C2×C3
LCSG ▷ C1
UCSC1 ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C8×C9×C13, C2×C42×C5×C9×C13, C23×C4×C5×C9×C13, …
maximal normal subgroup ofC22×C5×C8×C9×C13, C2×C42×C5×C9×C13, C23×C4×C5×C9×C13, …
maximal quotient ofC22×C5×C8×C9×C13, C2×C42×C5×C9×C13, C23×C4×C5×C9×C13, …
automorphism group ofC11×C19×C53, C11×C27×C53, C5×C27×C131, …
outer automorphism group ofC11×C19×C53, C11×C27×C53, C5×C27×C131, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.