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C7×#383⋊C3 #13055046

order1344
isoclinismisoclinic class of #126⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×#383⋊C3
unambiguous semidirect product#383⋊(C3×C7)

Splittings

Fitting, HallC7×#383 ⋊ C3
derivedC42 ⋊ C3×C4×C7
Sylow#383 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7#126⋊C3
commutator, hypocenterC42C3×C4×C7
FrattiniC23C2×C7×A4
FittingC7×#383C3
socleC23×C7C2×A4
prime radicalC2×C7×C42⋊C3C2
cosocleC2×C42C2×C3×C7
LCSG ▷ C42
UCSC1 ◁ C2×C7

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 168

A minimal faithful permutation representation — 2 generators on 27 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4335);