Finite Group Databasebeta

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C3×D5665 #46800922

order33990
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5665
unambiguous semidirect productC5⋊(C3×D1133)
unambiguous semidirect productC11⋊(C3×D515)

Splittings

Fitting, socle, HallC3×C5×C11×C103 ⋊ C2
derived, HallC5×C11×C103 ⋊ C2×C3
HallC3×C11×C103 ⋊ D5
HallC3×C5×C103 ⋊ D11
HallC11×C103 ⋊ C3×D5
HallC5×C103 ⋊ C3×D11
HallC3×C103 ⋊ D55
HallC3×C5×C11 ⋊ D103
SylowC103 ⋊ C3×D55
HallC5×C11 ⋊ C3×D103
HallC3×C11 ⋊ D515
HallC3×C5 ⋊ D1133
SylowC11 ⋊ C3×D515
SylowC5 ⋊ C3×D1133

Subgroups

subgroupG/H
center, hypercenterC3D5665
commutator, cosocle, hypocenterC5×C11×C103C2×C3
FrattiniC1G
Fitting, socleC3×C5×C11×C103C2
LCSG ▷ C5×C11×C103
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 122
transitive degreeμt(G) = 16995

A minimal faithful permutation representation — 2 generators on 122 points:

(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122);(5,8)(6,7)(10,19)(11,18)(12,17)(13,16)(14,15)(21,122)(22,121)(23,120)(24,119)(25,118)(26,117)(27,116)(28,115)(29,114)(30,113)(31,112)(32,111)(33,110)(34,109)(35,108)(36,107)(37,106)(38,105)(39,104)(40,103)(41,102)(42,101)(43,100)(44,99)(45,98)(46,97)(47,96)(48,95)(49,94)(50,93)(51,92)(52,91)(53,90)(54,89)(55,88)(56,87)(57,86)(58,85)(59,84)(60,83)(61,82)(62,81)(63,80)(64,79)(65,78)(66,77)(67,76)(68,75)(69,74)(70,73)(71,72)

Conjugacy classes & character table

8502 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33990, 11);