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C22⋊D5×C49 #14519926

order1960
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C49 · Schur multiplier (H2) = C2

Aliases

direct productC22⋊D5×C49
unambiguous semidirect productC22⋊(D5×C49)

Splittings

FittingC22×C5×C49 ⋊ C2
HallC5×C49 ⋊ D4
SylowC5 ⋊ D4×C49

Subgroups

subgroupG/H
centerC2×C49C2×D5
commutatorC2×C5C22×C49
FrattiniC2×C7C2×C7×D5
FittingC22×C5×C49C2
socle, cosocleC2×C5×C7C22×C7
prime radicalC7×C22⋊D5C7
hypercenterC22×C49D5
hypocenterC5D4×C49
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C49 ◁ C22×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 58
transitive degreeμt(G) = 980

A minimal faithful permutation representation — 2 generators on 58 points:

(1,2,4,5,3)(7,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58);(2,3)(4,5)(6,7)(8,9)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 23);