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C2×C25⋊(D67⋊C3) #34117162

order20100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25⋊(D67⋊C3)
unambiguous semidirect product(C2×C25)⋊(D67⋊C3)
unambiguous semidirect product(C2×C67⋊C3)⋊D25
unambiguous semidirect product(C2×D1675)⋊C3

Splittings

FittingC2×C25×C67 ⋊ C2×C3
derived, HallC25×C67 ⋊ C22×C3
HallC2×D1675 ⋊ C3
HallC25×C67⋊C3 ⋊ C22
HallC67⋊C3 ⋊ C2×D25
SylowC67 ⋊ C2×C3×D25
SylowC25 ⋊ C2×D67⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C25⋊(D67⋊C3)
commutator, cosocle, hypocenterC25×C67C22×C3
FrattiniC5C2×C5⋊(D67⋊C3)
FittingC2×C25×C67C2×C3
socleC2×C5×C67C3×D5
LCSG ▷ C25×C67
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 94
transitive degreeμt(G) = 3350

A minimal faithful permutation representation — 2 generators on 94 points:

(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,59)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,55,54,40,49,65)(34,62,63,50,48,56)(37,42,61,51,52,57)(53,60,66,58,64,67)(69,71)(70,74)(72,77)(73,80)(75,83)(76,82)(78,79)(81,87)(84,88)(85,89)(86,91)(90,92);(1,2,5,11,19,32,36,10,16,24,38,54,66,64,31,48,55,57,59,63,28,43,44,27,42,58,51,35,22,7,6,12,21,34,50,33,20,4,8,13,23,37,53,52,18,29,39,41,56,47,61,49,62,46,60,67,65,45,15,26,14,25,40,30,17,9,3)(68,82,92,85,71,74,88,86,77,80,83,81,79,78,87,75,73,72,91,84,70,69,89,90,76)(93,94)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20100, 18);