Finite Group Databasebeta

← Prev (#27210464) Next (#27210466) →

C13×Dic255 #27210465

order13260
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×Dic255
unambiguous semidirect productC3⋊(C13×Dic85)

Splittings

derived, HallC3×C5×C17 ⋊ C4×C13
HallC3×C5×C13×C17 ⋊ C4
HallC5×C13×C17 ⋊ Dic3
HallC3×C13×C17 ⋊ Dic5
HallC13×C17 ⋊ Dic15
HallC3×C5×C13 ⋊ Dic17
HallC5×C17 ⋊ Dic3×C13
HallC5×C13 ⋊ Dic51
HallC3×C17 ⋊ C13×Dic5
HallC3×C13 ⋊ Dic85
SylowC17 ⋊ C13×Dic15
HallC3×C5 ⋊ C13×Dic17
SylowC5 ⋊ C13×Dic51
SylowC3 ⋊ C13×Dic85

Subgroups

subgroupG/H
center, hypercenterC2×C13D255
commutator, hypocenterC3×C5×C17C4×C13
FrattiniC2C13×D255
Fitting, socle, prime radicalC2×C3×C5×C13×C17C2
cosocleC2×C3×C5×C17C2×C13
LCSG ▷ C3×C5×C17
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 13260

A minimal faithful permutation representation — 2 generators on 42 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(19,20)(21,22)(24,25)(26,27,28,29)(30,31,32,33,34,35,36,37,38,39,40,41,42);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(18,19,21,22,20)(23,24,25)

Conjugacy classes & character table

3354 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 15);