C₅×C₁₃×D₉₅ #27134705

order	12350
isoclinism	isoclinic class of D₉₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₃×D₉₅
unambiguous semidirect product	C₅⋊(C₅×C₁₃×D₁₉)
unambiguous semidirect product	C₁₉⋊(C₅×D₅×C₁₃)

Splittings

Fitting, socle, Hall	C₅²×C₁₃×C₁₉ ⋊ C₂
derived	C₅×C₁₉ ⋊ C₂×C₅×C₁₃
Hall	C₅²×C₁₉ ⋊ C₂×C₁₃
Hall	C₅²×C₁₃ ⋊ D₁₉
Hall	C₁₃×C₁₉ ⋊ C₅×D₅
Sylow	C₅² ⋊ C₁₃×D₁₉
Sylow	C₁₉ ⋊ C₅×D₅×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₉₅
commutator, cosocle, hypocenter	C₅×C₁₉	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₁₉	C₂
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₅×C₁₃

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 2470

A minimal faithful permutation representation — 2 generators on 42 points:

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

Conjugacy classes & character table

3185 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₅×C₁₃×D₁₉, C₅×D₁₃×D₉₅, C₅×D₆₅⋊D₁₉, …
maximal normal subgroup of	C₅×D₅×C₁₃×D₁₉, C₅×D₁₃×D₉₅, C₅×D₆₅⋊D₁₉, …
maximal quotient of	C₅×C₁₃×Dic₉₅, C₂×C₅×C₁₃×D₉₅, C₃×C₅×C₁₃×D₉₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12350, 16);

C5×C13×D95 #27134705