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C7×#401⋊C3 #13055053

order1344
isoclinismisoclinic class of #396⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#401⋊C3

Splittings

Fitting, HallC7×#401 ⋊ C3
Sylow#401 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7#126⋊C3
commutator, cosocle, hypocenter#95C2×C3×C7
FrattiniC23C2×C7×A4
FittingC7×#401C3
socleC23×C7C2×A4
prime radicalC7×#95⋊C3C2
LCSG ▷ #95
UCSC1 ◁ C2×C7

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 168

A minimal faithful permutation representation — 2 generators on 31 points:

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

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4342);