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C2×D6175 #37590785

order24700
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD12350
direct productC2×D6175
unambiguous semidirect product(C2×C13)⋊D475
unambiguous semidirect product(C2×C19)⋊D325
unambiguous semidirect product(C2×C25)⋊D247

Splittings

FittingC2×C13×C19×C25 ⋊ C2
derived, HallC13×C19×C25 ⋊ C22
HallC19×C25 ⋊ C2×D13
HallC13×C25 ⋊ C2×D19
HallC13×C19 ⋊ C2×D25
SylowC25 ⋊ C2×D247
SylowC19 ⋊ C2×D325
SylowC13 ⋊ C2×D475

Subgroups

subgroupG/H
center, hypercenterC2D6175
commutator, cosocle, hypocenterC13×C19×C25C22
FrattiniC5C2×D1235
FittingC2×C13×C19×C25C2
socleC2×C5×C13×C19D5
LCSG ▷ C13×C19×C25
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 59
transitive degreeμt(G) = 12350

A minimal faithful permutation representation — 2 generators on 59 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);(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)

Conjugacy classes & character table

6178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD24700
maximal normal subgroup ofD24700
maximal quotient ofDic12350, D24700

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24700, 29);