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C3×Dic1105 #27210459

order13260
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic1105

Splittings

derived, HallC5×C13×C17 ⋊ C3×C4
HallC3×C5×C13×C17 ⋊ C4
HallC3×C13×C17 ⋊ Dic5
HallC3×C5×C17 ⋊ Dic13
HallC13×C17 ⋊ C3×Dic5
HallC3×C5×C13 ⋊ Dic17
HallC5×C17 ⋊ C3×Dic13
HallC5×C13 ⋊ C3×Dic17
HallC3×C17 ⋊ Dic65
HallC3×C13 ⋊ Dic85
SylowC17 ⋊ C3×Dic65
HallC3×C5 ⋊ Dic221
SylowC13 ⋊ C3×Dic85
SylowC5 ⋊ C3×Dic221

Subgroups

subgroupG/H
center, hypercenterC2×C3D1105
commutator, hypocenterC5×C13×C17C3×C4
FrattiniC2C3×D1105
Fitting, socle, prime radicalC2×C3×C5×C13×C17C2
cosocleC2×C5×C13×C17C2×C3
LCSG ▷ C5×C13×C17
UCSC1 ◁ C2×C3

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)(36,39,38,37)(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)(31,32,34,35,33)

Conjugacy classes & character table

3324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 9);