Finite Group Databasebeta

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C4×C11×C239 #24901931

order10516
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C23×C5×C7×C17 (order 4760) · Inn(G) = C1 · Out(G) = C23×C5×C7×C17
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC10516
abelianC4×C11×C239

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C11×C239
socle, prime radicalC2×C11×C239C2
LCSG ▷ C1
UCSC1 ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10516 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic10516, D21032
maximal subgroup ofC3×C4×C11×C239, C8×C11×C239, C2×C4×C11×C239, …
maximal normal subgroup ofC3×C4×C11×C239, C8×C11×C239, C2×C4×C11×C239, …
maximal quotient ofC3×C4×C11×C239, C8×C11×C239, C2×C4×C11×C239

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10516, 1);