C₁₉×C₂₅×D₁₃ #27134692

order	12350
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₂₅×D₁₃
unambiguous semidirect product	C₁₃⋊(C₂×C₁₉×C₂₅)

Splittings

Fitting, Hall	C₁₃×C₁₉×C₂₅ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₁₉×C₂₅
Hall	C₁₃×C₂₅ ⋊ C₂×C₁₉
Hall	C₁₃×C₁₉ ⋊ C₂×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₂₅	D₁₃
commutator, hypocenter	C₁₃	C₂×C₁₉×C₂₅
Frattini	C₅	C₅×C₁₉×D₁₃
Fitting	C₁₃×C₁₉×C₂₅	C₂
socle	C₅×C₁₃×C₁₉	C₂×C₅
prime radical	C₅×C₁₉×D₁₃	C₅
cosocle	C₅×C₁₃	C₂×C₅×C₁₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₉×C₂₅

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 6175

A minimal faithful permutation representation — 2 generators on 57 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,17,20,24,16,18,21,25,29,19,22,26,30,33,23,27,31,34,36,28,32,35,37,38)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57);(1,2,4,6,8,10,12,13,11,9,7,5,3)

Conjugacy classes & character table

3800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×C₂₅×#261, C₂₅×C₁₉⋊#261, C₂₅×D₁₃×D₁₉, …
maximal normal subgroup of	C₁₉×C₂₅×#261, C₂₅×C₁₉⋊#261, C₂₅×D₁₃×D₁₉, …
maximal quotient of	C₁₉×C₂₅×Dic₁₃, C₂×C₁₉×C₂₅×D₁₃, C₃×C₁₉×C₂₅×D₁₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12350, 3);

C19×C25×D13 #27134692