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C7×#557⋊C3 #13060754

order1344
isoclinismisoclinic class of #548⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#557⋊C3
unambiguous semidirect product#557⋊(C3×C7)

Splittings

Fitting, HallC7×#557 ⋊ C3
Sylow#557 ⋊ C3×C7

Subgroups

subgroupG/H
center, socleC22×C7C22×A4
commutator, cosocleC2×Q8C22×C3×C7
FrattiniC22C22×C7×A4
FittingC7×#557C3
prime radicalC2×C7×SL(2,𝔽3)C22
hypercenterC7×C4⋊C4A4
hypocenterQ8C3×C7×Q8
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C7 ◁ C7×C4⋊C4

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 448

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

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

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10043);