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C7×#384⋊C3 #13055047

order1344
isoclinismisoclinic class of #127⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C4

Aliases

direct productC7×#384⋊C3
unambiguous semidirect product#384⋊(C3×C7)

Splittings

Fitting, HallC7×#384 ⋊ C3
derivedC42 ⋊ C3×C4×C7
Sylow#384 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7#127⋊C3
commutator, hypocenterC42C3×C4×C7
FrattiniC23C2×C7×A4
FittingC7×#384C3
socleC23×C7C2×A4
prime radicalC2×C7×C42⋊C3C2
cosocleC2×C42C2×C3×C7
LCSG ▷ C42
UCSC1 ◁ C2×C7

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 168

A minimal faithful permutation representation — 2 generators on 23 points:

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

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, 4336);