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3−1+2×D37 #14522003

order1998
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C1

Aliases

direct product3−1+2×D37

Splittings

Fitting, Hall3−1+2×C37 ⋊ C2
SylowC37 ⋊ C2×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×D37
commutator, socle, cosocleC3×C37C2×C32
Fitting3−1+2×C37C2
prime radicalC32×D37C3
hypercenter3−1+2D37
hypocenterC37C2×3−1+2
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C3 ◁ 3−1+2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 333

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2,4,3,6,8,7,5,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46);(2,5,6)(4,8,9)(11,46)(12,45)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1998, 33);