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C3×Dic50 #10597034

order600
isoclinismisoclinic class of Dic50
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic50
unambiguous semidirect productC25⋊(C3×Q8)

Splittings

HallC3×C25 ⋊ Q8
SylowC25 ⋊ C3×Q8

Subgroups

subgroupG/H
centerC2×C3C2×D25
commutator, cosocleC2×C25C22×C3
FrattiniC2×C5C2×C3×D5
FittingC3×C4×C25C2
socle, prime radicalC2×C3×C5C2×D5
hypercenterC3×C4D25
hypocenterC25C3×Q8
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C2×C3 ◁ C3×C4

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 600

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

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

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11924802, #11924804, #11924809, …
maximal normal subgroup of#11924802, #11924804, #11924809, …
maximal quotient ofC3×#87718, C3×C4⋊Dic25, C2×C3×Dic50, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(600, 15);