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C11×(C2×D7)⋊C4 #11927673

order1232
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C22

Aliases

direct productC11×(C2×D7)⋊C4
unambiguous semidirect product(C2×D7)⋊(C4×C11)

Splittings

FittingC2×C4×C7×C11 ⋊ C2
HallC7×C11 ⋊ C22⋊C4
SylowC7 ⋊ C11×C22⋊C4

Subgroups

subgroupG/H
centerC22×C11C2×D7
commutatorC2×C7C2×C4×C11
FrattiniC22C2×C11×D7
FittingC2×C4×C7×C11C2
socleC22×C7×C11C22
prime radicalC22×C11×D7C2
cosocleC22×C7C22×C11
hypercenterC2×C4×C11D7
hypocenterC7C11×C22⋊C4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C11 ◁ C2×C4×C11

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 616

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,17,18,16,14)(19,20,21,22)(24,26);(13,14)(15,16)(17,18)(23,24)(25,26)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1232, 56);