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C7×#376⋊C3 #13055044

order1344
isoclinismisoclinic class of #95⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×#376⋊C3
unambiguous semidirect product#376⋊(C3×C7)

Splittings

Fitting, HallC7×#376 ⋊ C3
Sylow#376 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC4×C7C42⋊C3
commutator, cosocle, hypocenter#95C2×C3×C7
FrattiniC23C2×C7×A4
FittingC7×#376C3
socleC23×C7C2×A4
prime radicalC7×#95⋊C3C2
LCSG ▷ #95
UCSC1 ◁ C4×C7

86 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)(8,13,27,15,10,21,12,24,16,9,19,30)(11,23,26,25,18,31,20,22,28,14,17,29);(8,11,12,20)(9,14,15,25)(16,26)(17,18)(21,29)(22,23)(27,28)(30,31)

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4333);