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C2×D4255 #30684453

order17020
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD8510
direct productC2×D4255
unambiguous semidirect product(C2×C5)⋊D851
unambiguous semidirect product(C2×C23)⋊D185
unambiguous semidirect product(C2×C37)⋊D115

Splittings

Fitting, socleC2×C5×C23×C37 ⋊ C2
derived, HallC5×C23×C37 ⋊ C22
HallC23×C37 ⋊ C2×D5
HallC5×C37 ⋊ C2×D23
HallC5×C23 ⋊ C2×D37
SylowC37 ⋊ C2×D115
SylowC23 ⋊ C2×D185
SylowC5 ⋊ C2×D851

Subgroups

subgroupG/H
center, hypercenterC2D4255
commutator, cosocle, hypocenterC5×C23×C37C22
FrattiniC1G
Fitting, socleC2×C5×C23×C37C2
LCSG ▷ C5×C23×C37
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 67
transitive degreeμt(G) = 8510

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);(4,7)(5,6)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)

Conjugacy classes & character table

4258 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD17020, C2×D12765
maximal normal subgroup ofD17020
maximal quotient ofDic8510, D17020, C2×D12765

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17020, 29);