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C2×D3895 #29510015

order15580
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD7790
direct productC2×D3895
unambiguous semidirect product(C2×C5)⋊D779
unambiguous semidirect product(C2×C19)⋊D205
unambiguous semidirect product(C2×C41)⋊D95

Splittings

Fitting, socleC2×C5×C19×C41 ⋊ C2
derived, HallC5×C19×C41 ⋊ C22
HallC19×C41 ⋊ C2×D5
HallC5×C41 ⋊ C2×D19
HallC5×C19 ⋊ C2×D41
SylowC41 ⋊ C2×D95
SylowC19 ⋊ C2×D205
SylowC5 ⋊ C2×D779

Subgroups

subgroupG/H
center, hypercenterC2D3895
commutator, cosocle, hypocenterC5×C19×C41C22
FrattiniC1G
Fitting, socleC2×C5×C19×C41C2
LCSG ▷ C5×C19×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 67
transitive degreeμt(G) = 7790

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

Conjugacy classes & character table

3898 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD15580
maximal normal subgroup ofD15580
maximal quotient ofDic7790, D15580

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15580, 40);