C₅×D₁₁₉ #11924733

order	1190
isoclinism	isoclinic class of D₁₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₁₁₉
unambiguous semidirect product	C₇⋊(C₅×D₁₇)
unambiguous semidirect product	C₁₇⋊(C₅×D₇)

Splittings

Fitting, socle, Hall	C₅×C₇×C₁₇ ⋊ C₂
derived, Hall	C₇×C₁₇ ⋊ C₂×C₅
Hall	C₅×C₁₇ ⋊ D₇
Hall	C₅×C₇ ⋊ D₁₇
Sylow	C₁₇ ⋊ C₅×D₇
Sylow	C₇ ⋊ C₅×D₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₅	D₁₁₉
commutator, cosocle, hypocenter	C₇×C₁₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₇	C₂
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₅

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 595

A minimal faithful permutation representation — 2 generators on 29 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);(7,12)(8,11)(9,10)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×D₇×D₁₇, D₅×D₁₁₉, D₃₅⋊D₁₇, …
maximal normal subgroup of	C₅×D₇×D₁₇, D₅×D₁₁₉, D₃₅⋊D₁₇, …
maximal quotient of	C₅×Dic₁₁₉, C₂×C₅×D₁₁₉, C₃×C₅×D₁₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1190, 3);

C5×D119 #11924733