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C2×D8099 #44569327

order32396
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16198
direct productC2×D8099
unambiguous semidirect product(C2×C7)⋊D1157
unambiguous semidirect product(C2×C13)⋊D623
unambiguous semidirect product(C2×C89)⋊D91

Splittings

Fitting, socleC2×C7×C13×C89 ⋊ C2
derived, HallC7×C13×C89 ⋊ C22
HallC13×C89 ⋊ C2×D7
HallC7×C89 ⋊ C2×D13
HallC7×C13 ⋊ C2×D89
SylowC89 ⋊ C2×D91
SylowC13 ⋊ C2×D623
SylowC7 ⋊ C2×D1157

Subgroups

subgroupG/H
center, hypercenterC2D8099
commutator, cosocle, hypocenterC7×C13×C89C22
FrattiniC1G
Fitting, socleC2×C7×C13×C89C2
LCSG ▷ C7×C13×C89
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 111
transitive degreeμt(G) = 16198

A minimal faithful permutation representation — 2 generators on 111 points:

(1,2)(3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(4,9)(5,8)(6,7)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(24,111)(25,110)(26,109)(27,108)(28,107)(29,106)(30,105)(31,104)(32,103)(33,102)(34,101)(35,100)(36,99)(37,98)(38,97)(39,96)(40,95)(41,94)(42,93)(43,92)(44,91)(45,90)(46,89)(47,88)(48,87)(49,86)(50,85)(51,84)(52,83)(53,82)(54,81)(55,80)(56,79)(57,78)(58,77)(59,76)(60,75)(61,74)(62,73)(63,72)(64,71)(65,70)(66,69)(67,68)

Conjugacy classes & character table

8102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD32396
maximal normal subgroup ofD32396
maximal quotient ofDic16198, D32396

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32396, 35);