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C2×D5593 #36375403

order22372
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11186
direct productC2×D5593
unambiguous semidirect product(C2×C7)⋊D799
unambiguous semidirect product(C2×C17)⋊D329
unambiguous semidirect product(C2×C47)⋊D119

Splittings

Fitting, socleC2×C7×C17×C47 ⋊ C2
derived, HallC7×C17×C47 ⋊ C22
HallC17×C47 ⋊ C2×D7
HallC7×C47 ⋊ C2×D17
HallC7×C17 ⋊ C2×D47
SylowC47 ⋊ C2×D119
SylowC17 ⋊ C2×D329
SylowC7 ⋊ C2×D799

Subgroups

subgroupG/H
center, hypercenterC2D5593
commutator, cosocle, hypocenterC7×C17×C47C22
FrattiniC1G
Fitting, socleC2×C7×C17×C47C2
LCSG ▷ C7×C17×C47
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 11186

A minimal faithful permutation representation — 2 generators on 73 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);(4,9)(5,8)(6,7)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(28,73)(29,72)(30,71)(31,70)(32,69)(33,68)(34,67)(35,66)(36,65)(37,64)(38,63)(39,62)(40,61)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)

Conjugacy classes & character table

5596 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD22372
maximal normal subgroup ofD22372
maximal quotient ofDic11186, D22372

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22372, 27);