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C3×C17×#63120 #27210537

order13260
isoclinismisoclinic class of #63120
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×#63120

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, HallC5×C13 ⋊ C3×C4×C17
HallC5×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ AGL(1,𝔽5)
HallC3×C5×C17 ⋊ Dic13
HallC13×C17 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C13 ⋊ C4×C17
HallC5×C17 ⋊ C3×Dic13
HallC3×C13 ⋊ C17×AGL(1,𝔽5)
HallC3×C5 ⋊ C17×Dic13
SylowC13 ⋊ C3×C17×AGL(1,𝔽5)
SylowC5 ⋊ C3×C17×Dic13

Subgroups

subgroupG/H
center, hypercenterC3×C17#63120
commutator, hypocenterC5×C13C3×C4×C17
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×D5×C13×C17C2
cosocleD5×C13C2×C3×C17
LCSG ▷ C5×C13
UCSC1 ◁ C3×C17

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

Conjugacy classes & character table

1479 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 87);