Finite Group Databasebeta

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C2×D14245 #72292111

order56980
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD28490
direct productC2×D14245

Splittings

Fitting, socleC2×C5×C7×C11×C37 ⋊ C2
derived, HallC5×C7×C11×C37 ⋊ C22
HallC7×C11×C37 ⋊ C2×D5
HallC5×C11×C37 ⋊ C2×D7
HallC5×C7×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×D35
HallC5×C7×C11 ⋊ C2×D37
HallC7×C37 ⋊ C2×D55
HallC5×C37 ⋊ C2×D77
HallC7×C11 ⋊ C2×D185
HallC5×C11 ⋊ C2×D259
SylowC37 ⋊ C2×D385
HallC5×C7 ⋊ C2×D407
SylowC11 ⋊ C2×D1295
SylowC7 ⋊ C2×D2035
SylowC5 ⋊ C2×D2849

Subgroups

subgroupG/H
center, hypercenterC2D14245
commutator, cosocle, hypocenterC5×C7×C11×C37C22
FrattiniC1G
Fitting, socleC2×C5×C7×C11×C37C2
LCSG ▷ C5×C7×C11×C37
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 62
transitive degreeμt(G) = 28490

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

Conjugacy classes & character table

14248 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((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), (4,7)(5,6)(9,14)(10,13)(11,12)(16,25)(17,24)(18,23)(19,22)(20,21)(27,62)(28,61)(29,60)(30,59)(31,58)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45));