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C2×D5735 #37525756

order22940
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11470
direct productC2×D5735
unambiguous semidirect product(C2×C5)⋊D1147
unambiguous semidirect product(C2×C31)⋊D185
unambiguous semidirect product(C2×C37)⋊D155

Splittings

Fitting, socleC2×C5×C31×C37 ⋊ C2
derived, HallC5×C31×C37 ⋊ C22
HallC31×C37 ⋊ C2×D5
HallC5×C37 ⋊ C2×D31
HallC5×C31 ⋊ C2×D37
SylowC37 ⋊ C2×D155
SylowC31 ⋊ C2×D185
SylowC5 ⋊ C2×D1147

Subgroups

subgroupG/H
center, hypercenterC2D5735
commutator, cosocle, hypocenterC5×C31×C37C22
FrattiniC1G
Fitting, socleC2×C5×C31×C37C2
LCSG ▷ C5×C31×C37
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 75
transitive degreeμt(G) = 11470

A minimal faithful permutation representation — 2 generators on 75 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);(4,7)(5,6)(9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(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

5738 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD22940
maximal normal subgroup ofD22940
maximal quotient ofDic11470, D22940

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22940, 46);