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C3×#87712 #11924825

order1200
isoclinismisoclinic class of Dic50
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#87712

Splittings

FittingC3×C8×C25 ⋊ C2
HallC3×C25 ⋊ M16
SylowC25 ⋊ C3×M16

Subgroups

subgroupG/H
centerC3×C4C2×D25
commutatorC2×C25C2×C3×C4
FrattiniC4×C5C2×C3×D5
FittingC3×C8×C25C2
socleC2×C3×C5C4×D5
prime radicalC2×C3×D25C4
cosocleC4×C25C22×C3
hypercenterC3×C8D25
hypocenterC25C3×M16
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C3×C4 ◁ C3×C8

60 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)(4,24,15,27,12,10,17,8,26,7,19,9,25,21,16,11,5,28,13,23,6,18,22,14,20)(29,30,31,34,32,33,35,36);(5,7)(6,10)(8,13)(9,16)(11,19)(12,18)(14,15)(17,23)(20,24)(21,25)(22,27)(26,28)(30,33)(34,36)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 35);