Finite Group Databasebeta

← Prev (#30630477) Next (#30630479) →

C2×D3995 #30630478

order15980
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD7990
direct productC2×D3995
unambiguous semidirect product(C2×C5)⋊D799
unambiguous semidirect product(C2×C17)⋊D235
unambiguous semidirect product(C2×C47)⋊D85

Splittings

Fitting, socleC2×C5×C17×C47 ⋊ C2
derived, HallC5×C17×C47 ⋊ C22
HallC17×C47 ⋊ C2×D5
HallC5×C47 ⋊ C2×D17
HallC5×C17 ⋊ C2×D47
SylowC47 ⋊ C2×D85
SylowC17 ⋊ C2×D235
SylowC5 ⋊ C2×D799

Subgroups

subgroupG/H
center, hypercenterC2D3995
commutator, cosocle, hypocenterC5×C17×C47C22
FrattiniC1G
Fitting, socleC2×C5×C17×C47C2
LCSG ▷ C5×C17×C47
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 71
transitive degreeμt(G) = 7990

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

Conjugacy classes & character table

3998 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD15980
maximal normal subgroup ofD15980
maximal quotient ofDic7990, D15980

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15980, 29);