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C2×D6365 #38764284

order25460
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD12730
direct productC2×D6365
unambiguous semidirect product(C2×C5)⋊D1273
unambiguous semidirect product(C2×C19)⋊D335
unambiguous semidirect product(C2×C67)⋊D95

Splittings

Fitting, socleC2×C5×C19×C67 ⋊ C2
derived, HallC5×C19×C67 ⋊ C22
HallC19×C67 ⋊ C2×D5
HallC5×C67 ⋊ C2×D19
HallC5×C19 ⋊ C2×D67
SylowC67 ⋊ C2×D95
SylowC19 ⋊ C2×D335
SylowC5 ⋊ C2×D1273

Subgroups

subgroupG/H
center, hypercenterC2D6365
commutator, cosocle, hypocenterC5×C19×C67C22
FrattiniC1G
Fitting, socleC2×C5×C19×C67C2
LCSG ▷ C5×C19×C67
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 93
transitive degreeμt(G) = 12730

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

Conjugacy classes & character table

6368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD25460
maximal normal subgroup ofD25460
maximal quotient ofDic12730, D25460

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25460, 27);