Finite Group Databasebeta

← Prev (#27211532) Next (#27211534) →

D33×C29⋊C7 #27211533

order13398
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productD33×C29⋊C7
unambiguous semidirect productC3⋊(D11×C29⋊C7)
unambiguous semidirect productC11⋊(D3×C29⋊C7)
unambiguous semidirect product(C29×D33)⋊C7

Splittings

Fitting, socle, derived, HallC3×C11×C29 ⋊ C2×C7
HallC3×C11×C29⋊C7 ⋊ C2
HallC11×C29⋊C7 ⋊ D3
HallC29×D33 ⋊ C7
HallC3×C29⋊C7 ⋊ D11
HallC11×C29 ⋊ D3×C7
HallC3×C29 ⋊ C7×D11
HallC3×C11 ⋊ C2×C29⋊C7
SylowC29 ⋊ C7×D33
SylowC11 ⋊ D3×C29⋊C7
SylowC3 ⋊ D11×C29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C29C2×C7
LCSG ▷ C3×C11×C29
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 957

A minimal faithful permutation representation — 2 generators on 43 points:

(2,3,5,8,9,15,20)(4,7,12,19,27,6,10)(11,18,16,24,28,14,17)(13,21,23,26,25,22,29)(31,32)(33,34)(35,36)(37,38)(39,40)(42,43);(1,2,4,7,13,22,21,8,14,23,24,10,17,25,19,28,3,6,11,12,20,27,29,15,5,9,16,18,26)(30,31,33,35,37,39,40,38,36,34,32)(41,42,43)

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD33×D29⋊C7, D33⋊(D29⋊C7), D3×D11×C29⋊C7, …
maximal normal subgroup ofD33×D29⋊C7, D33⋊(D29⋊C7), D3×D11×C29⋊C7, …
maximal quotient ofDic33×C29⋊C7, C2×D33×C29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 24);