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D25×D43⋊C3 #27166347

order12900
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD25×D43⋊C3
unambiguous semidirect productD43⋊(C3×D25)
unambiguous semidirect product(D25×D43)⋊C3
unambiguous semidirect product(C25×D43⋊C3)⋊C2
unambiguous semidirect product(D25×C43⋊C3)⋊C2
unambiguous semidirect product(C25⋊(D43⋊C3))⋊C2

Splittings

Fitting, derived, HallC25×C43 ⋊ C22×C3
HallD25×D43 ⋊ C3
HallC25×C43⋊C3 ⋊ C22
HallC43⋊C3 ⋊ C2×D25
SylowC43 ⋊ C2×C3×D25
SylowC25 ⋊ C2×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC25×C43C22×C3
FrattiniC5D5×D43⋊C3
socleC5×C43C2×C3×D5
LCSG ▷ C25×C43
UCSC1

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 68
transitive degreeμt(G) = 1075

A minimal faithful permutation representation — 2 generators on 68 points:

(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,36)(12,26,22,20,16,13)(19,32,34,23,25,37)(21,38,39,30,29,33)(31,41,42,40,35,43)(44,49,64,63,47,46,57,67,53,52,51,66,61,54,60,59,58,48,62,65,50,45,55,68,56);(1,2,5,11,19,22,7,6,12,21,31,39,15,26,14,25,35,42,28,37,38,27,18,29,34,36,43,41,32,10,16,24,33,40,30,20,4,8,13,23,17,9,3)(45,47)(46,50)(48,53)(49,56)(51,59)(52,58)(54,61)(55,63)(57,65)(60,66)(62,67)(64,68)

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 16);