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C3×C5×C13×Dic17 #27210453

order13260
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C13×Dic17

Splittings

derived, SylowC17 ⋊ C3×C4×C5×C13
HallC3×C5×C13×C17 ⋊ C4
HallC5×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ C4×C5
HallC3×C5×C17 ⋊ C4×C13
HallC13×C17 ⋊ C3×C4×C5
HallC5×C17 ⋊ C3×C4×C13
HallC3×C17 ⋊ C4×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C13D17
commutator, hypocenterC17C3×C4×C5×C13
FrattiniC2C3×C5×C13×D17
Fitting, socle, prime radicalC2×C3×C5×C13×C17C2
cosocleC2×C17C2×C3×C5×C13
LCSG ▷ C17
UCSC1 ◁ C2×C3×C5×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)(18,21,20,19)(22,23,24,25,26,27,28,29,30,31,32,33,34)(35,36,37,38,39)(40,41,42);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 3);