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C2×Q16×C13⋊C3 #11928739

order1248
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC2×Q16×C13⋊C3
unambiguous semidirect product(C2×C13×Q16)⋊C3

Splittings

Fitting, HallC2×C13×Q16 ⋊ C3
SylowC13 ⋊ C2×C3×Q16

Subgroups

subgroupG/H
centerC22D4×C13⋊C3
commutator, cosocleC4×C13C23×C3
FrattiniC4C23×C13⋊C3
FittingC2×C13×Q16C3
socleC22×C13C3×D4
prime radicalC22×C13⋊C3D4
hypercenterC2×Q16C13⋊C3
hypocenterC13C2×C3×Q16
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 416

A minimal faithful permutation representation — 3 generators on 31 points:

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 851);