Finite Group Databasebeta

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C22×C3×C4×C9×C29 #72190874

order12528
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 580608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C3×C4×C9×C29
multiplicative(ℤ/14573)ˣ, (ℤ/15281)ˣ, (ℤ/18305)ˣ, (ℤ/19647)ˣ, (ℤ/19893)ˣ, (ℤ/20397)ˣ, (ℤ/20709)ˣ, (ℤ/23535)ˣ, (ℤ/26524)ˣ, (ℤ/27196)ˣ, (ℤ/29146)ˣ, (ℤ/30562)ˣ, (ℤ/36610)ˣ, (ℤ/37692)ˣ, (ℤ/39294)ˣ, (ℤ/39786)ˣ, (ℤ/40794)ˣ, (ℤ/41418)ˣ, (ℤ/47070)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C23×C32×C29
socle, prime radicalC23×C32×C29C2×C3
LCSG ▷ C1
UCSC1 ◁ G

540 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C8×C9×C29, C2×C3×C42×C9×C29, C23×C3×C4×C9×C29
maximal normal subgroup ofC22×C3×C8×C9×C29, C2×C3×C42×C9×C29, C23×C3×C4×C9×C29
maximal quotient ofC22×C3×C8×C9×C29, C2×C3×C42×C9×C29, C23×C3×C4×C9×C29
automorphism group ofC13×C19×C59, C7×C37×C59, C5×C7×C523, …
outer automorphism group ofC13×C19×C59, C7×C37×C59, C5×C7×C523, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.