Finite Group Databasebeta

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C3×C4×C8×C9×C13 #72189713

order11232
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 165888
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C4

Aliases

abelianC3×C4×C8×C9×C13
multiplicative(ℤ/11461)ˣ, (ℤ/11581)ˣ, (ℤ/12181)ˣ, (ℤ/12337)ˣ, (ℤ/22922)ˣ, (ℤ/23162)ˣ, (ℤ/24362)ˣ, (ℤ/24674)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C4C22×C32×C13
socle, prime radicalC22×C32×C13C2×C3×C4
LCSG ▷ C1
UCSC1 ◁ G

440 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C9×C13×C16, C3×C82×C9×C13, C2×C3×C4×C8×C9×C13
maximal normal subgroup ofC3×C4×C9×C13×C16, C3×C82×C9×C13, C2×C3×C4×C8×C9×C13
maximal quotient ofC3×C4×C9×C13×C16, C3×C82×C9×C13, C2×C3×C4×C8×C9×C13
automorphism group ofC73×C157, C37×C313, C13×C937
outer automorphism group ofC73×C157, C37×C313, C13×C937

GAP

Past the SmallGroups library coverage — no SmallGroups id.