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C3×C5×Dic221 #27210455

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

Aliases

direct productC3×C5×Dic221

Splittings

derived, HallC13×C17 ⋊ C3×C4×C5
HallC3×C5×C13×C17 ⋊ C4
HallC5×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ C4×C5
HallC3×C5×C17 ⋊ Dic13
HallC3×C5×C13 ⋊ Dic17
HallC5×C17 ⋊ C3×Dic13
HallC5×C13 ⋊ C3×Dic17
HallC3×C17 ⋊ C5×Dic13
HallC3×C13 ⋊ C5×Dic17
SylowC17 ⋊ C3×C5×Dic13
SylowC13 ⋊ C3×C5×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D221
commutator, hypocenterC13×C17C3×C4×C5
FrattiniC2C3×C5×D221
Fitting, socle, prime radicalC2×C3×C5×C13×C17C2
cosocleC2×C13×C17C2×C3×C5
LCSG ▷ C13×C17
UCSC1 ◁ C2×C3×C5

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)(31,34,33,32)(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)(18,19,21,23,25,27,29,30,28,26,24,22,20)

Conjugacy classes & character table

3360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 5);