C₅×C₁₇×D₇₃ #27137196

order	12410
isoclinism	isoclinic class of D₇₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₇×D₇₃
unambiguous semidirect product	C₇₃⋊(C₂×C₅×C₁₇)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₁₇	D₇₃
commutator, cosocle, hypocenter	C₇₃	C₂×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₇₃	C₂
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₅×C₁₇

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);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)

Conjugacy classes & character table

3230 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₁₇×#64408, C₅×#19097221, C₅×D₁₇×D₇₃, …
maximal normal subgroup of	C₅×C₁₇×#64408, C₅×#19097221, C₅×D₁₇×D₇₃, …
maximal quotient of	C₅×C₁₇×Dic₇₃, C₂×C₅×C₁₇×D₇₃, C₃×C₅×C₁₇×D₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12410, 2);

C5×C17×D73 #27137196