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C2×D4403 #31798569

order17612
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD8806
direct productC2×D4403
unambiguous semidirect product(C2×C7)⋊D629
unambiguous semidirect product(C2×C17)⋊D259
unambiguous semidirect product(C2×C37)⋊D119

Splittings

Fitting, socleC2×C7×C17×C37 ⋊ C2
derived, HallC7×C17×C37 ⋊ C22
HallC17×C37 ⋊ C2×D7
HallC7×C37 ⋊ C2×D17
HallC7×C17 ⋊ C2×D37
SylowC37 ⋊ C2×D119
SylowC17 ⋊ C2×D259
SylowC7 ⋊ C2×D629

Subgroups

subgroupG/H
center, hypercenterC2D4403
commutator, cosocle, hypocenterC7×C17×C37C22
FrattiniC1G
Fitting, socleC2×C7×C17×C37C2
LCSG ▷ C7×C17×C37
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 8806

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

Conjugacy classes & character table

4406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD17612, C2×D13209
maximal normal subgroup ofD17612
maximal quotient ofDic8806, D17612, C2×D13209

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17612, 29);