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C5×C7×C19×Dic5 #27210874

order13300
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C19 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C19×Dic5

Splittings

derivedC5 ⋊ C4×C5×C7×C19
HallC52×C7×C19 ⋊ C4
HallC52×C19 ⋊ C4×C7
HallC52×C7 ⋊ C4×C19
SylowC52 ⋊ C4×C7×C19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C19D5
commutator, hypocenterC5C4×C5×C7×C19
FrattiniC2C5×C7×D5×C19
Fitting, socle, prime radicalC2×C52×C7×C19C2
cosocleC2×C5C2×C5×C7×C19
LCSG ▷ C5
UCSC1 ◁ C2×C5×C7×C19

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 2660

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5)(7,8)(9,10)(11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33)(34,35,36,37,38,39,40);(6,7,9,10,8)

Conjugacy classes & character table

5320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 32);