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C2×D6105 #37567647

order24420
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD12210
direct productC2×D6105
unambiguous semidirect product(C2×C3)⋊D2035
unambiguous semidirect product(C2×C5)⋊D1221
unambiguous semidirect product(C2×C11)⋊D555
unambiguous semidirect product(C2×C37)⋊D165

Splittings

Fitting, socleC2×C3×C5×C11×C37 ⋊ C2
derived, HallC3×C5×C11×C37 ⋊ C22
HallC5×C11×C37 ⋊ C2×D3
HallC3×C11×C37 ⋊ C2×D5
HallC3×C5×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×D15
HallC5×C37 ⋊ C2×D33
HallC3×C5×C11 ⋊ C2×D37
HallC3×C37 ⋊ C2×D55
HallC5×C11 ⋊ C2×D111
SylowC37 ⋊ C2×D165
HallC3×C11 ⋊ C2×D185
HallC3×C5 ⋊ C2×D407
SylowC11 ⋊ C2×D555
SylowC5 ⋊ C2×D1221
SylowC3 ⋊ C2×D2035

Subgroups

subgroupG/H
center, hypercenterC2D6105
commutator, cosocle, hypocenterC3×C5×C11×C37C22
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C37C2
LCSG ▷ C3×C5×C11×C37
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 58
transitive degreeμt(G) = 12210

A minimal faithful permutation representation — 2 generators on 58 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);(4,5)(7,10)(8,9)(12,21)(13,20)(14,19)(15,18)(16,17)(23,58)(24,57)(25,56)(26,55)(27,54)(28,53)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)

Conjugacy classes & character table

6108 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD24420
maximal normal subgroup ofD24420
maximal quotient ofDic12210, D24420

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 168);