Finite Group Databasebeta

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C5×D3399 #46800926

order33990
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3399
unambiguous semidirect productC3⋊(C5×D1133)
unambiguous semidirect productC103⋊(C5×D33)

Splittings

Fitting, socle, HallC3×C5×C11×C103 ⋊ C2
derived, HallC3×C11×C103 ⋊ C2×C5
HallC5×C11×C103 ⋊ D3
HallC3×C5×C103 ⋊ D11
HallC11×C103 ⋊ C5×D3
HallC5×C103 ⋊ D33
HallC3×C103 ⋊ C5×D11
HallC3×C5×C11 ⋊ D103
SylowC103 ⋊ C5×D33
HallC5×C11 ⋊ D309
HallC3×C11 ⋊ C5×D103
HallC3×C5 ⋊ D1133
SylowC11 ⋊ C5×D309
SylowC3 ⋊ C5×D1133

Subgroups

subgroupG/H
center, hypercenterC5D3399
commutator, cosocle, hypocenterC3×C11×C103C2×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C103C2
LCSG ▷ C3×C11×C103
UCSC1 ◁ C5

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);(7,8)(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

8505 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33990, 15);