C₃×C₂₅×D₁₇ #14579339

order	2550
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₂₅×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×C₃×C₂₅)

Splittings

Fitting, Hall	C₃×C₁₇×C₂₅ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₃×C₂₅
Hall	C₁₇×C₂₅ ⋊ C₂×C₃
Hall	C₃×C₁₇ ⋊ C₂×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₅	D₁₇
commutator, hypocenter	C₁₇	C₂×C₃×C₂₅
Frattini	C₅	C₃×C₅×D₁₇
Fitting	C₃×C₁₇×C₂₅	C₂
socle	C₃×C₅×C₁₇	C₂×C₅
prime radical	C₃×C₅×D₁₇	C₅
cosocle	C₅×C₁₇	C₂×C₃×C₅
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃×C₂₅

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1275

A minimal faithful permutation representation — 2 generators on 45 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₇×C₂₅×D₁₇, C₃×C₂₅×D₁₁₉, ΓL(1,𝔽₈)×C₂₅×D₁₇, …
maximal normal subgroup of	C₃×C₇×C₂₅×D₁₇, C₃×C₁₁×C₂₅×D₁₇, C₃×C₁₃×C₂₅×D₁₇
maximal quotient of	C₃×C₇×C₂₅×D₁₇, C₃×C₂₅×D₁₁₉, ΓL(1,𝔽₈)×C₂₅×D₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2550, 2);

C3×C25×D17 #14579339