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Cayley diagram

C11×C3⋊Dic3 #87682

order396
isoclinismisoclinic class of C3⋊D3
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×C3⋊Dic3
unambiguous semidirect productC3⋊(C11×Dic3)

Splittings

derived, SylowC32 ⋊ C4×C11
HallC32×C11 ⋊ C4

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊D3
commutator, hypocenterC32C4×C11
FrattiniC2C11×C3⋊D3
Fitting, socle, prime radicalC2×C32×C11C2
cosocleC2×C32C2×C11
LCSG ▷ C32
UCSC1 ◁ C2×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 396

A minimal faithful permutation representation — 3 generators on 21 points:

(1,4,3,2)(6,7)(9,10)(11,12,13,14,15,16,17,18,19,20,21);(8,9,10);(5,6,7)

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

derived subgroup of#13097228, #13097229, #13097230, …
maximal subgroup ofC11×#622, C11⋊#622, D11×C3⋊Dic3, …
maximal normal subgroup ofC11×#622, C11⋊#622, D11×C3⋊Dic3, …
maximal quotient ofC11×C3⋊(C3⋊C8), C2×C11×C3⋊Dic3, C11×C3⋊Dic9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(396, 14);