C₃×Dic₉₅ #11765879

order	1140
isoclinism	isoclinic class of D₉₅
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×Dic₉₅

Splittings

derived, Hall	C₅×C₁₉ ⋊ C₃×C₄
Hall	C₃×C₅×C₁₉ ⋊ C₄
Hall	C₃×C₁₉ ⋊ Dic₅
Sylow	C₁₉ ⋊ C₃×Dic₅
Hall	C₃×C₅ ⋊ Dic₁₉
Sylow	C₅ ⋊ C₃×Dic₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₉₅
commutator, hypocenter	C₅×C₁₉	C₃×C₄
Frattini	C₂	C₃×D₉₅
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₉	C₂
cosocle	C₂×C₅×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1140

A minimal faithful permutation representation — 2 generators on 31 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);(4,6,5,7)(9,12)(10,11)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#4294⋊Dic₅, C₉×Dic₉₅, C₃×(C₁₉⋊C₃)⋊Dic₅, …
maximal normal subgroup of	#4294⋊Dic₅, C₉×Dic₉₅, C₃×(C₁₉⋊C₃)⋊Dic₅, …
maximal quotient of	C₉×Dic₉₅, C₃²×Dic₉₅, C₃×Dic₂₈₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1140, 7);

C3×Dic95 #11765879