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C2×D5775 #37528327

order23100
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11550
direct productC2×D5775
unambiguous semidirect product(C2×C3)⋊D1925
unambiguous semidirect product(C2×C7)⋊D825
unambiguous semidirect product(C2×C11)⋊D525
unambiguous semidirect product(C2×C25)⋊D231

Splittings

FittingC2×C3×C7×C11×C25 ⋊ C2
derived, HallC3×C7×C11×C25 ⋊ C22
HallC7×C11×C25 ⋊ C2×D3
HallC3×C11×C25 ⋊ C2×D7
HallC3×C7×C25 ⋊ C2×D11
HallC11×C25 ⋊ C2×D21
HallC3×C7×C11 ⋊ C2×D25
HallC7×C25 ⋊ C2×D33
HallC7×C11 ⋊ C2×D75
HallC3×C25 ⋊ C2×D77
HallC3×C11 ⋊ C2×D175
SylowC25 ⋊ C2×D231
HallC3×C7 ⋊ C2×D275
SylowC11 ⋊ C2×D525
SylowC7 ⋊ C2×D825
SylowC3 ⋊ C2×D1925

Subgroups

subgroupG/H
center, hypercenterC2D5775
commutator, cosocle, hypocenterC3×C7×C11×C25C22
FrattiniC5C2×D1155
FittingC2×C3×C7×C11×C25C2
socleC2×C3×C5×C7×C11D5
LCSG ▷ C3×C7×C11×C25
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 11550

A minimal faithful permutation representation — 2 generators on 48 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);(4,5)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(32,37)(33,36)(34,35)(39,48)(40,47)(41,46)(42,45)(43,44)

Conjugacy classes & character table

5778 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23100
maximal normal subgroup ofD23100
maximal quotient ofDic11550, D23100

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 138);