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C2×D7975 #44542005

order31900
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15950
direct productC2×D7975
unambiguous semidirect product(C2×C11)⋊D725
unambiguous semidirect product(C2×C25)⋊D319
unambiguous semidirect product(C2×C29)⋊D275

Splittings

FittingC2×C11×C25×C29 ⋊ C2
derived, HallC11×C25×C29 ⋊ C22
HallC25×C29 ⋊ C2×D11
HallC11×C29 ⋊ C2×D25
HallC11×C25 ⋊ C2×D29
SylowC29 ⋊ C2×D275
SylowC25 ⋊ C2×D319
SylowC11 ⋊ C2×D725

Subgroups

subgroupG/H
center, hypercenterC2D7975
commutator, cosocle, hypocenterC11×C25×C29C22
FrattiniC5C2×D1595
FittingC2×C11×C25×C29C2
socleC2×C5×C11×C29D5
LCSG ▷ C11×C25×C29
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 67
transitive degreeμt(G) = 15950

A minimal faithful permutation representation — 2 generators on 67 points:

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

Conjugacy classes & character table

7978 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD31900
maximal normal subgroup ofD31900
maximal quotient ofDic15950, D31900

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31900, 40);