Finite Group Databasebeta

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C11⋊(C17⋊(D31⋊C3)) #46852041

order34782
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊(C17⋊(D31⋊C3))
unambiguous semidirect productC17⋊(C11⋊(D31⋊C3))
unambiguous semidirect product(C31⋊C3)⋊D187
unambiguous semidirect productD5797⋊C3

Splittings

Fitting, socle, derived, HallC11×C17×C31 ⋊ C2×C3
HallC11×C17×C31⋊C3 ⋊ C2
HallD5797 ⋊ C3
HallC17×C31⋊C3 ⋊ D11
HallC11×C31⋊C3 ⋊ D17
HallC17×C31 ⋊ C3×D11
HallC11×C31 ⋊ C3×D17
HallC11×C17 ⋊ D31⋊C3
HallC31⋊C3 ⋊ D187
SylowC31 ⋊ C3×D187
SylowC17 ⋊ C11⋊(D31⋊C3)
SylowC11 ⋊ C17⋊(D31⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C17×C31C2×C3
LCSG ▷ C11×C17×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 59
transitive degreeμt(G) = 5797

A minimal faithful permutation representation — 2 generators on 59 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(30,34,35,31,32,36)(33,42,43,37,38,50)(39,52,53,45,46,58)(40,51,47,48,44,41)(49,59,56,55,54,57);(1,2,4,6,8,10,11,9,7,5,3)(12,13,15,17,19,21,23,25,27,28,26,24,22,20,18,16,14)(29,30,33,39,47,35,34,40,49,56,43,51,42,46,54,53,58,59,52,38,44,50,57,55,48,32,36,41,45,37,31)

Polycyclic presentation:

2,3,11,17,31|c^a=c^10,d^a=d^16,e^a=e^30,e^b=e^25

Conjugacy classes & character table

1220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34782, 24);