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C2×D5945 #37558113

order23780
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11890
direct productC2×D5945
unambiguous semidirect product(C2×C5)⋊D1189
unambiguous semidirect product(C2×C29)⋊D205
unambiguous semidirect product(C2×C41)⋊D145

Splittings

Fitting, socleC2×C5×C29×C41 ⋊ C2
derived, HallC5×C29×C41 ⋊ C22
HallC29×C41 ⋊ C2×D5
HallC5×C41 ⋊ C2×D29
HallC5×C29 ⋊ C2×D41
SylowC41 ⋊ C2×D145
SylowC29 ⋊ C2×D205
SylowC5 ⋊ C2×D1189

Subgroups

subgroupG/H
center, hypercenterC2D5945
commutator, cosocle, hypocenterC5×C29×C41C22
FrattiniC1G
Fitting, socleC2×C5×C29×C41C2
LCSG ▷ C5×C29×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 77
transitive degreeμt(G) = 11890

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

Conjugacy classes & character table

5948 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23780
maximal normal subgroup ofD23780
maximal quotient ofDic11890, D23780

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23780, 66);