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C2×C43⋊(D31⋊C5) #40998622

order26660
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C43⋊(D31⋊C5)
unambiguous semidirect product(C2×C43)⋊(D31⋊C5)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊D43
unambiguous semidirect product(C2×D1333)⋊C5

Splittings

Fitting, socleC2×C31×C43 ⋊ C2×C5
derived, HallC31×C43 ⋊ C22×C5
HallC43×ΓL(1,𝔽32) ⋊ C22
HallC2×D1333 ⋊ C5
HallΓL(1,𝔽32) ⋊ C2×D43
SylowC43 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C5×D43

Subgroups

subgroupG/H
center, hypercenterC2C43⋊(D31⋊C5)
commutator, cosocle, hypocenterC31×C43C22×C5
FrattiniC1G
Fitting, socleC2×C31×C43C2×C5
LCSG ▷ C31×C43
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 76
transitive degreeμt(G) = 2666

A minimal faithful permutation representation — 2 generators on 76 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26660, 16);