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C2×D5863 #37553009

order23452
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11726
direct productC2×D5863
unambiguous semidirect product(C2×C11)⋊D533
unambiguous semidirect product(C2×C13)⋊D451
unambiguous semidirect product(C2×C41)⋊D143

Splittings

Fitting, socleC2×C11×C13×C41 ⋊ C2
derived, HallC11×C13×C41 ⋊ C22
HallC13×C41 ⋊ C2×D11
HallC11×C41 ⋊ C2×D13
HallC11×C13 ⋊ C2×D41
SylowC41 ⋊ C2×D143
SylowC13 ⋊ C2×D451
SylowC11 ⋊ C2×D533

Subgroups

subgroupG/H
center, hypercenterC2D5863
commutator, cosocle, hypocenterC11×C13×C41C22
FrattiniC1G
Fitting, socleC2×C11×C13×C41C2
LCSG ▷ C11×C13×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 67
transitive degreeμt(G) = 11726

A minimal faithful permutation representation — 2 generators on 67 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60)(36,59)(37,58)(38,57)(39,56)(40,55)(41,54)(42,53)(43,52)(44,51)(45,50)(46,49)(47,48)

Conjugacy classes & character table

5866 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23452
maximal normal subgroup ofD23452
maximal quotient ofDic11726, D23452

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23452, 35);