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C3×C17×Dic65 #27210458

order13260
isoclinismisoclinic class of D65
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×Dic65

Splittings

derived, HallC5×C13 ⋊ C3×C4×C17
HallC3×C5×C13×C17 ⋊ C4
HallC5×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ Dic5
HallC3×C5×C17 ⋊ Dic13
HallC13×C17 ⋊ C3×Dic5
HallC3×C5×C13 ⋊ C4×C17
HallC5×C17 ⋊ C3×Dic13
HallC3×C13 ⋊ C17×Dic5
HallC3×C5 ⋊ C17×Dic13
SylowC13 ⋊ C3×C17×Dic5
SylowC5 ⋊ C3×C17×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D65
commutator, hypocenterC5×C13C3×C4×C17
FrattiniC2C3×C17×D65
Fitting, socle, prime radicalC2×C3×C5×C13×C17C2
cosocleC2×C5×C13C2×C3×C17
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C17

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

Conjugacy classes & character table

3468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 8);