Finite Group Databasebeta

← Prev (#38759761) Next (#38759763) →

C2×D6305 #38759762

order25220
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD12610
direct productC2×D6305
unambiguous semidirect product(C2×C5)⋊D1261
unambiguous semidirect product(C2×C13)⋊D485
unambiguous semidirect product(C2×C97)⋊D65

Splittings

Fitting, socleC2×C5×C13×C97 ⋊ C2
derived, HallC5×C13×C97 ⋊ C22
HallC13×C97 ⋊ C2×D5
HallC5×C97 ⋊ C2×D13
SylowC97 ⋊ C2×D65
HallC5×C13 ⋊ C2×D97
SylowC13 ⋊ C2×D485
SylowC5 ⋊ C2×D1261

Subgroups

subgroupG/H
center, hypercenterC2D6305
commutator, cosocle, hypocenterC5×C13×C97C22
FrattiniC1G
Fitting, socleC2×C5×C13×C97C2
LCSG ▷ C5×C13×C97
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 117
transitive degreeμt(G) = 12610

A minimal faithful permutation representation — 2 generators on 117 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117);(4,7)(5,6)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(22,117)(23,116)(24,115)(25,114)(26,113)(27,112)(28,111)(29,110)(30,109)(31,108)(32,107)(33,106)(34,105)(35,104)(36,103)(37,102)(38,101)(39,100)(40,99)(41,98)(42,97)(43,96)(44,95)(45,94)(46,93)(47,92)(48,91)(49,90)(50,89)(51,88)(52,87)(53,86)(54,85)(55,84)(56,83)(57,82)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71)(69,70)

Conjugacy classes & character table

6308 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD25220
maximal normal subgroup ofD25220
maximal quotient ofDic12610, D25220

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25220, 51);