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C3×#67267 #11764162

order1104
isoclinismisoclinic class of Dic46
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#67267

Splittings

HallC3×C23 ⋊ M16
SylowC23 ⋊ C3×M16

Subgroups

subgroupG/H
centerC3×C4C2×D23
commutatorC2×C23C2×C3×C4
FrattiniC4C2×C3×D23
FittingC2×C3×C4×C23C2
socleC2×C3×C23C2×C4
prime radicalC22×C3×C23C4
cosocleC4×C23C22×C3
hypercenterC2×C3×C4D23
hypocenterC23C3×M16
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

40 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)(28,31)(32,34);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28,29,32,30,31,33,34)

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, 37);