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3−1+2×D25 #13062448

order1350
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C1

Aliases

direct product3−1+2×D25
unambiguous semidirect productC25⋊(C2×3−1+2)
unambiguous semidirect product(C9×D25)⋊C3

Splittings

Fitting, HallC25×3−1+2 ⋊ C2
SylowC25 ⋊ C2×3−1+2

Subgroups

subgroupG/H
centerC3C32×D25
commutator, cosocleC3×C25C2×C32
Frattini, socleC3×C5C32×D5
FittingC25×3−1+2C2
prime radicalC32×D25C3
hypercenter3−1+2D25
hypocenterC25C2×3−1+2
LCSG ▷ C3×C25 ▷ C25
UCSC1 ◁ C3 ◁ 3−1+2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 225

A minimal faithful permutation representation — 2 generators on 34 points:

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

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup of3−1+2×#1035, 3−1+2×D25⋊C5, D25×AGL(1,ℤ/9), …
maximal normal subgroup of3−1+2×#1035, 3−1+2×D25⋊C5, D25×AGL(1,ℤ/9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1350, 7);