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2−1+4×C13⋊C3 #11929251

order1248
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct product2−1+4×C13⋊C3

Splittings

Fitting, HallC13×2−1+4 ⋊ C3
SylowC13 ⋊ C3×2−1+4

Subgroups

subgroupG/H
center, FrattiniC2C24×C13⋊C3
commutator, socle, cosocleC2×C13C24×C3
FittingC13×2−1+4C3
hypercenter2−1+4C13⋊C3
hypocenterC13C3×2−1+4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ 2−1+4

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 208

A minimal faithful permutation representation — 4 generators on 29 points:

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

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1363);