C₃³×D₂₅ #13062473

order	1350
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³ · Schur multiplier (H₂) = C₃³

Aliases

direct product	C₃³×D₂₅
unambiguous semidirect product	C₂₅⋊(C₂×C₃³)

Splittings

Fitting, Hall	C₃³×C₂₅ ⋊ C₂
derived, Sylow	C₂₅ ⋊ C₂×C₃³

Subgroups

	subgroup	G/H
center, hypercenter	C₃³	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₃³
Frattini	C₅	C₃³×D₅
Fitting	C₃³×C₂₅	C₂
socle	C₃³×C₅	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃³

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 675

A minimal faithful permutation representation — 3 generators on 34 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1350, 32);

C33×D25 #13062473