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C2×C25×D43⋊C3 #27166348

order12900
isoclinismisoclinic class of D43⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×D43⋊C3
unambiguous semidirect productD43⋊(C2×C3×C25)
unambiguous semidirect product(C43⋊C3)⋊(C22×C25)
unambiguous semidirect product(C2×D43)⋊(C3×C25)
unambiguous semidirect product(C2×C43⋊C3)⋊(C2×C25)
unambiguous semidirect product(C2×C25×D43)⋊C3

Splittings

FittingC2×C25×C43 ⋊ C2×C3
derived, SylowC43 ⋊ C22×C3×C25
HallC2×C25×D43 ⋊ C3
HallC25×C43⋊C3 ⋊ C22
HallC25×C43 ⋊ C22×C3
HallC2×D43 ⋊ C3×C25
HallC43⋊C3 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25D43⋊C3
commutator, hypocenterC43C22×C3×C25
FrattiniC5C2×C5×D43⋊C3
FittingC2×C25×C43C2×C3
socleC2×C5×C43C2×C3×C5
prime radicalC2×C5×D43⋊C3C5
cosocleC5×C43C22×C3×C5
LCSG ▷ C43
UCSC1 ◁ C2×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 70
transitive degreeμt(G) = 2150

A minimal faithful permutation representation — 2 generators on 70 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)(44,48,56,64,68,46,52,61,67,54,49,57,65,50,59,53,62,47,55,63,58,45,51,60,66);(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)(69,70)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 17);