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M16×C31⋊C3 #13093456

order1488
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productM16×C31⋊C3
unambiguous semidirect product(M16×C31)⋊C3

Splittings

Fitting, HallM16×C31 ⋊ C3
SylowC31 ⋊ C3×M16

Subgroups

subgroupG/H
center, FrattiniC4C22×C31⋊C3
commutator, socleC2×C31C2×C3×C4
FittingM16×C31C3
prime radicalC22×C31⋊C3C4
cosocleC4×C31C22×C3
hypercenterM16C31⋊C3
hypocenterC31C3×M16
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ M16

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 248

A minimal faithful permutation representation — 2 generators on 39 points:

(1,2,3,4,5,6,7,8)(10,11,13)(12,15,20)(14,18,17)(16,22,29)(19,25,27)(21,23,24)(26,32,36)(28,33,34)(30,37,31)(35,38,39);(2,6)(4,8)(9,10,12,16,23,13,17,24,31,37,20,27,34,22,30,29,36,39,32,15,21,28,35,38,25,11,14,19,26,33,18)

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1488, 52);