Finite Group Databasebeta

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C3×C8×C11×C37 #72188479

order9768
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C24×C4×C5×C9 (order 2880) · Inn(G) = C1 · Out(G) = C24×C4×C5×C9
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC9768
abelianC3×C8×C11×C37
multiplicative(ℤ/9769)ˣ, (ℤ/19538)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C2×C3×C11×C37
socle, prime radicalC2×C3×C11×C37C4
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9768 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic9768, D19536
maximal subgroup ofC3×C11×C16×C37, C2×C3×C8×C11×C37, C8×C9×C11×C37, …
maximal normal subgroup ofC3×C11×C16×C37, C2×C3×C8×C11×C37, C8×C9×C11×C37, …
maximal quotient ofC3×C11×C16×C37, C2×C3×C8×C11×C37, C8×C9×C11×C37, …
automorphism group ofC9769
outer automorphism group ofC9769

GAP

Past the SmallGroups library coverage — no SmallGroups id.