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C5×#67267 #14270255

order1840
isoclinismisoclinic class of Dic46
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#67267

Splittings

HallC5×C23 ⋊ M16
SylowC23 ⋊ C5×M16

Subgroups

subgroupG/H
centerC4×C5C2×D23
commutatorC2×C23C2×C4×C5
FrattiniC4C2×C5×D23
FittingC2×C4×C5×C23C2
socleC2×C5×C23C2×C4
prime radicalC22×C5×C23C4
cosocleC4×C23C22×C5
hypercenterC2×C4×C5D23
hypocenterC23C5×M16
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C4×C5 ◁ C2×C4×C5

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 920

A minimal faithful permutation representation — 2 generators on 36 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1840, 38);