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C2×D4495 #31822905

order17980
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD8990
direct productC2×D4495
unambiguous semidirect product(C2×C5)⋊D899
unambiguous semidirect product(C2×C29)⋊D155
unambiguous semidirect product(C2×C31)⋊D145

Splittings

Fitting, socleC2×C5×C29×C31 ⋊ C2
derived, HallC5×C29×C31 ⋊ C22
HallC29×C31 ⋊ C2×D5
HallC5×C31 ⋊ C2×D29
HallC5×C29 ⋊ C2×D31
SylowC31 ⋊ C2×D145
SylowC29 ⋊ C2×D155
SylowC5 ⋊ C2×D899

Subgroups

subgroupG/H
center, hypercenterC2D4495
commutator, cosocle, hypocenterC5×C29×C31C22
FrattiniC1G
Fitting, socleC2×C5×C29×C31C2
LCSG ▷ C5×C29×C31
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 67
transitive degreeμt(G) = 8990

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)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)

Conjugacy classes & character table

4498 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD17980, C2×D13485
maximal normal subgroup ofD17980
maximal quotient ofDic8990, D17980, C2×D13485

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17980, 40);