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C2×D2945 #26044536

order11780
automorphismAut(G) order 12722400
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD5890
direct productC2×D2945
unambiguous semidirect product(C2×C5)⋊D589
unambiguous semidirect product(C2×C19)⋊D155
unambiguous semidirect product(C2×C31)⋊D95

Splittings

Fitting, socleC2×C5×C19×C31 ⋊ C2
derived, HallC5×C19×C31 ⋊ C22
HallC19×C31 ⋊ C2×D5
HallC5×C31 ⋊ C2×D19
HallC5×C19 ⋊ C2×D31
SylowC31 ⋊ C2×D95
SylowC19 ⋊ C2×D155
SylowC5 ⋊ C2×D589

Subgroups

subgroupG/H
center, hypercenterC2D2945
commutator, cosocle, hypocenterC5×C19×C31C22
FrattiniC1G
Fitting, socleC2×C5×C19×C31C2
LCSG ▷ C5×C19×C31
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 5890

A minimal faithful permutation representation — 2 generators on 57 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);(4,7)(5,6)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(28,57)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)

Conjugacy classes & character table

2948 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊#16812976, C2×C5⋊#16812975, C2×C5⋊((C19⋊C3)⋊D31), …
maximal normal subgroup ofC2×C5⋊#16812976, C2×C5⋊#16812975, C2×C5⋊((C19⋊C3)⋊D31), …
maximal quotient ofD3×D2945, C2×C3×D2945, C2×D8835, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11780, 30);