Finite Group Databasebeta

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C3×#89294 #13051159

order1344
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C1

Aliases

direct productC3×#89294

Splittings

HallC3×C7 ⋊ M64
SylowC7 ⋊ C3×M64

Subgroups

subgroupG/H
centerC3×C16C2×D7
commutatorC2×C7C2×C3×C16
FrattiniC16C2×C3×D7
FittingC2×C3×C7×C16C2
socleC2×C3×C7C2×C16
prime radicalC22×C3×C7C16
cosocleC7×C16C22×C3
hypercenterC2×C3×C16D7
hypocenterC7C3×M64
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C3×C16 ◁ C2×C3×C16

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 672

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3)(4,5,7,9,10,8,6)(12,17)(18,27)(19,28)(20,29)(30,37)(31,38)(32,39)(40,42);(5,6)(7,8)(9,10)(11,12,13,18,14,19,21,30,15,20,22,31,24,32,33,40,16,17,23,27,25,28,34,37,26,29,35,38,36,39,41,42)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 448);