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C3×C5×#11725132 #27210522

order13260
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×#11725132

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, HallC13×C17 ⋊ C3×C4×C5
HallC5×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ C4×C5
HallC3×C5×C17 ⋊ #261
HallC3×C5×C13 ⋊ Dic17
HallC5×C17 ⋊ C3×#261
HallC5×C13 ⋊ C3×Dic17
HallC3×C17 ⋊ C5×#261
HallC3×C13 ⋊ C5×Dic17
SylowC17 ⋊ C3×C5×#261
SylowC13 ⋊ C3×C5×Dic17

Subgroups

subgroupG/H
center, hypercenterC3×C5#11725132
commutator, hypocenterC13×C17C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×C5×C17×D13C2
cosocleC17×D13C2×C3×C5
LCSG ▷ C13×C17
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 3315

A minimal faithful permutation representation — 2 generators on 38 points:

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

Conjugacy classes & character table

1065 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 72);