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C2×C5×#15693307 #45684466

order33180
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×#15693307

Splittings

Fitting, socleC2×C5×C7×C79 ⋊ C2×C3
derived, HallC7×C79 ⋊ C22×C3×C5
HallC2×C5×D553 ⋊ C3
HallC5×#13110306 ⋊ C22
HallC5×C7×C79 ⋊ C22×C3
HallC2×D553 ⋊ C3×C5
Hall#13110306 ⋊ C22×C5
HallC5×C79 ⋊ C2×AGL(1,𝔽7)
SylowC79 ⋊ C2×C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×D79⋊C3
SylowC7 ⋊ C2×C5×D79⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#15693307
commutator, cosocle, hypocenterC7×C79C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C79C2×C3
LCSG ▷ C7×C79
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 93
transitive degreeμt(G) = 5530

A minimal faithful permutation representation — 2 generators on 93 points:

(3,4,5,6,7)(9,12,13,10,11,14)(16,20,21,17,18,22)(19,28,29,23,24,38)(25,41,42,31,32,55)(26,40,36,34,30,27)(33,60,61,44,45,76)(35,58,59,47,43,52)(37,39,57,49,50,53)(46,81,82,63,64,92)(48,79,80,66,62,74)(51,56,78,68,65,75)(54,87,86,71,72,70)(67,88,89,73,83,90)(69,77,93,84,85,91);(1,2)(8,9,11,14,13,12,10)(15,16,19,25,33,46,65,32,43,53,55,74,89,61,78,87,79,60,77,84,68,49,36,21,20,26,35,48,67,71,50,24,30,38,52,70,82,93,64,83,88,81,91,92,86,59,29,40,28,39,54,73,66,47,34,18,22,27,37,51,69,85,45,62,72,75,76,90,80,42,57,58,41,56,63,44,31,23,17)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 97);