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C5×#21439686 #50303704

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

Aliases

direct productC5×#21439686

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C3×C4
derived, HallC72×C13 ⋊ C3×C4×C5
HallC5×#14579330 ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C4
Hall#14579330 ⋊ C3×C5
HallC72×C13⋊C3 ⋊ C4×C5
HallC5×C72 ⋊ AGL(1,𝔽13)
HallC5×C13⋊C3 ⋊ #5997
HallC5×C13 ⋊ C3×#5997
SylowC72 ⋊ C5×AGL(1,𝔽13)
HallC13⋊C3 ⋊ C5×#5997
SylowC13 ⋊ C3×C5×#5997

Subgroups

subgroupG/H
center, hypercenterC5#21439686
commutator, hypocenterC72×C13C3×C4×C5
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalC5×(C13⋊C3)⋊(C7⋊D7)C2
cosocleC7⋊D91C2×C3×C5
LCSG ▷ C72×C13
UCSC1 ◁ C5

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 910

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 390);