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#41×C52⋊C3 #11925668

order1200
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C5

Aliases

direct product#41×C52⋊C3

Splittings

Fitting, HallC52×#41 ⋊ C3
SylowC52 ⋊ C3×#41

Subgroups

subgroupG/H
centerC4C22×C52⋊C3
commutator, socle, cosocleC2×C52C23×C3
FrattiniC2C23×C52⋊C3
FittingC52×#41C3
hypercenter#41C52⋊C3
hypocenterC52C3×#41
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C4 ◁ #41

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 3 generators on 23 points:

(1,2)(3,6)(4,5)(7,8)(9,10,12)(11,15,17)(13,18,21)(14,20,23)(16,19,22);(2,5)(6,8)(9,11,16,21,23)(10,15,19,13,14)(12,18,17,20,22);(1,3,4,7)(2,6,5,8)

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 878);