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#101×C13⋊C3 #11928012

order1248
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct product#101×C13⋊C3
unambiguous semidirect product(C13×#101)⋊C3

Splittings

Fitting, HallC13×#101 ⋊ C3
SylowC13 ⋊ C3×#101

Subgroups

subgroupG/H
centerC2C22⋊C4×C13⋊C3
commutatorC22×C13C2×C3×C4
FrattiniC2×C4C22×C13⋊C3
FittingC13×#101C3
socleC2×C13C3×C22⋊C4
prime radicalC22×C13⋊C3C2×C4
cosocleC2×C4×C13C22×C3
hypercenter#101C13⋊C3
hypocenterC13C3×#101
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 124);