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C2×D3335 #27211124

order13340
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD6670
direct productC2×D3335
unambiguous semidirect product(C2×C5)⋊D667
unambiguous semidirect product(C2×C23)⋊D145
unambiguous semidirect product(C2×C29)⋊D115

Splittings

Fitting, socleC2×C5×C23×C29 ⋊ C2
derived, HallC5×C23×C29 ⋊ C22
HallC23×C29 ⋊ C2×D5
HallC5×C29 ⋊ C2×D23
HallC5×C23 ⋊ C2×D29
SylowC29 ⋊ C2×D115
SylowC23 ⋊ C2×D145
SylowC5 ⋊ C2×D667

Subgroups

subgroupG/H
center, hypercenterC2D3335
commutator, cosocle, hypocenterC5×C23×C29C22
FrattiniC1G
Fitting, socleC2×C5×C23×C29C2
LCSG ▷ C5×C23×C29
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 59
transitive degreeμt(G) = 6670

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

Conjugacy classes & character table

3338 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD13340
maximal normal subgroup ofD13340
maximal quotient ofD13340, Dic6670

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13340, 29);