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C3×C5×#14579330 #50304337

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C7

Aliases

direct productC3×C5×#14579330

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derived, HallC72×C13 ⋊ C3×C4×C5
HallC5×C72×C13 ⋊ C3×C4
HallC3×C72×C13 ⋊ C4×C5
HallC3×C5×C72 ⋊ #261
HallC5×C72 ⋊ C3×#261
HallC3×C5×C13 ⋊ #5997
HallC3×C72 ⋊ C5×#261
HallC5×C13 ⋊ C3×#5997
SylowC72 ⋊ C3×C5×#261
HallC3×C13 ⋊ C5×#5997
SylowC13 ⋊ C3×C5×#5997

Subgroups

subgroupG/H
center, hypercenterC3×C5#14579330
commutator, hypocenterC72×C13C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C5×C7⋊D91C2
cosocleC7⋊D91C2×C3×C5
LCSG ▷ C72×C13
UCSC1 ◁ C3×C5

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 2730

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

2445 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1023);