Finite Group Databasebeta

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C23×C4×C9×C41 #72190268

order11808
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5160960
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C4×C9×C41
multiplicative(ℤ/23655)ˣ, (ℤ/24568)ˣ, (ℤ/25232)ˣ, (ℤ/29560)ˣ, (ℤ/31540)ˣ, (ℤ/35472)ˣ, (ℤ/35856)ˣ, (ℤ/36852)ˣ, (ℤ/44340)ˣ, (ℤ/44820)ˣ, (ℤ/47310)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C24×C3×C41
socle, prime radicalC24×C3×C41C2×C3
LCSG ▷ C1
UCSC1 ◁ G

708 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11808 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C8×C9×C41, C22×C42×C9×C41, C24×C4×C9×C41
maximal normal subgroup ofC23×C8×C9×C41, C22×C42×C9×C41, C24×C4×C9×C41
maximal quotient ofC23×C8×C9×C41, C22×C42×C9×C41, C24×C4×C9×C41
automorphism group ofC8×C37×C83, C16×C19×C83, C5×C8×C739
outer automorphism group ofC8×C37×C83, C16×C19×C83, C5×C8×C739

GAP

Past the SmallGroups library coverage — no SmallGroups id.