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C3×C13×C17×Dic5 #27210456

order13260
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C3×C4×C13×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×C17×Dic5

Splittings

derived, SylowC5 ⋊ C3×C4×C13×C17
HallC3×C5×C13×C17 ⋊ C4
HallC5×C13×C17 ⋊ C3×C4
HallC3×C5×C17 ⋊ C4×C13
HallC3×C5×C13 ⋊ C4×C17
HallC5×C17 ⋊ C3×C4×C13
HallC5×C13 ⋊ C3×C4×C17
HallC3×C5 ⋊ C4×C13×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13×C17D5
commutator, hypocenterC5C3×C4×C13×C17
FrattiniC2C3×D5×C13×C17
Fitting, socle, prime radicalC2×C3×C5×C13×C17C2
cosocleC2×C5C2×C3×C13×C17
LCSG ▷ C5
UCSC1 ◁ C2×C3×C13×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)(6,9,8,7)(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);(1,2,4,5,3)

Conjugacy classes & character table

5304 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 6);