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C5×Dic663 #27210463

order13260
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic663
unambiguous semidirect productC3⋊(C5×Dic221)

Splittings

derived, HallC3×C13×C17 ⋊ C4×C5
HallC3×C5×C13×C17 ⋊ C4
HallC5×C13×C17 ⋊ Dic3
HallC3×C5×C17 ⋊ Dic13
HallC13×C17 ⋊ C5×Dic3
HallC3×C5×C13 ⋊ Dic17
HallC5×C17 ⋊ Dic39
HallC5×C13 ⋊ Dic51
HallC3×C17 ⋊ C5×Dic13
HallC3×C13 ⋊ C5×Dic17
SylowC17 ⋊ C5×Dic39
HallC3×C5 ⋊ Dic221
SylowC13 ⋊ C5×Dic51
SylowC3 ⋊ C5×Dic221

Subgroups

subgroupG/H
center, hypercenterC2×C5D663
commutator, hypocenterC3×C13×C17C4×C5
FrattiniC2C5×D663
Fitting, socle, prime radicalC2×C3×C5×C13×C17C2
cosocleC2×C3×C13×C17C2×C5
LCSG ▷ C3×C13×C17
UCSC1 ◁ C2×C5

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)(23,24)(25,26)(27,28)(29,30)(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)(18,19,21,23,25,27,29,30,28,26,24,22,20)(31,32,33)

Conjugacy classes & character table

3330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 13);