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C3×(C2×D23)⋊C4 #11764166

order1104
isoclinismisoclinic class of Dic46
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×(C2×D23)⋊C4
unambiguous semidirect product(C2×D23)⋊(C3×C4)

Splittings

FittingC2×C3×C4×C23 ⋊ C2
HallC3×C23 ⋊ C22⋊C4
SylowC23 ⋊ C3×C22⋊C4

Subgroups

subgroupG/H
centerC22×C3C2×D23
commutatorC2×C23C2×C3×C4
FrattiniC22C2×C3×D23
FittingC2×C3×C4×C23C2
socleC22×C3×C23C22
prime radicalC22×C3×D23C2
cosocleC22×C23C22×C3
hypercenterC2×C3×C4D23
hypocenterC23C3×C22⋊C4
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 552

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3)(4,5,7,9,11,13,15,17,19,21,23,25,26,24,22,20,18,16,14,12,10,8,6)(27,28,29,30)(32,34);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(31,32)(33,34)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1104, 41);