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C3×#88155 #11928791

order1248
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#88155

Splittings

FittingC2×C3×C8×C13 ⋊ C2
HallC3×C13 ⋊ #131
SylowC13 ⋊ C3×#131

Subgroups

subgroupG/H
centerC3×C8C2×D13
commutatorC2×C13C22×C3×C4
FrattiniC4C22×C3×D13
FittingC2×C3×C8×C13C2
socleC2×C3×C13C22×C4
prime radicalC3×#6127C2
cosocleC4×C13C23×C3
hypercenterC2×C3×C8D13
hypocenterC13C3×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C3×C8 ◁ C2×C3×C8

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 624

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 903);