D₅×C₁₇×C₇₃ #27137199

order	12410
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅×C₁₇×C₇₃
unambiguous semidirect product	C₅⋊(C₂×C₁₇×C₇₃)

Splittings

Fitting, socle, Hall	C₅×C₁₇×C₇₃ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂×C₁₇×C₇₃
Hall	C₅×C₇₃ ⋊ C₂×C₁₇
Hall	C₅×C₁₇ ⋊ C₂×C₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇×C₇₃	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₁₇×C₇₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₇₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₇×C₇₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 6205

A minimal faithful permutation representation — 2 generators on 95 points:

(2,3)(4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(1,2,4,5,3)

Conjugacy classes & character table

4964 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₇×AGL(1,𝔽₅)×C₇₃, C₁₇×#13091734, C₇₃×#66774, …
maximal normal subgroup of	C₁₇×AGL(1,𝔽₅)×C₇₃, C₁₇×#13091734, C₇₃×#66774, …
maximal quotient of	C₁₇×Dic₅×C₇₃, C₂×D₅×C₁₇×C₇₃, C₃×D₅×C₁₇×C₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12410, 5);

D5×C17×C73 #27137199