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3−1+2×D23 #11927854

order1242
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C1

Aliases

direct product3−1+2×D23
unambiguous semidirect productC23⋊(C2×3−1+2)
unambiguous semidirect product(C9×D23)⋊C3

Splittings

Fitting, HallC23×3−1+2 ⋊ C2
SylowC23 ⋊ C2×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×D23
commutator, socle, cosocleC3×C23C2×C32
FittingC23×3−1+2C2
prime radicalC32×D23C3
hypercenter3−1+2D23
hypocenterC23C2×3−1+2
LCSG ▷ C3×C23 ▷ C23
UCSC1 ◁ C3 ◁ 3−1+2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 207

A minimal faithful permutation representation — 2 generators on 32 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);(2,5,6)(4,8,9)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD23×AGL(1,ℤ/9), 3−1+2×AGL(1,𝔽23)
maximal normal subgroup ofD23×AGL(1,ℤ/9), 3−1+2×AGL(1,𝔽23)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1242, 7);