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C5⋊(C11⋊(D103⋊C3)) #46800944

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

Aliases

unambiguous semidirect productC5⋊(C11⋊(D103⋊C3))
unambiguous semidirect productC11⋊(C5⋊(D103⋊C3))
unambiguous semidirect product(C103⋊C3)⋊D55
unambiguous semidirect productD5665⋊C3

Splittings

Fitting, socle, derived, HallC5×C11×C103 ⋊ C2×C3
HallC5×C11×C103⋊C3 ⋊ C2
HallD5665 ⋊ C3
HallC11×C103⋊C3 ⋊ D5
HallC5×C103⋊C3 ⋊ D11
HallC11×C103 ⋊ C3×D5
HallC5×C103 ⋊ C3×D11
HallC103⋊C3 ⋊ D55
SylowC103 ⋊ C3×D55
HallC5×C11 ⋊ D103⋊C3
SylowC11 ⋊ C5⋊(D103⋊C3)
SylowC5 ⋊ C11⋊(D103⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C11×C103C2×C3
LCSG ▷ C5×C11×C103
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 119
transitive degreeμt(G) = 5665

A minimal faithful permutation representation — 2 generators on 119 points:

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

Polycyclic presentation:

2,3,5,11,103|c^a=c^4,d^a=d^10,e^a=e^102,e^b=e^56

Conjugacy classes & character table

1022 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33990, 33);