C₁₃×C₄₁⋊C₂₅ #27211017

order	13325
automorphism	?
homology	Abelianization (H₁) = C₁₃×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₄₁⋊C₂₅
unambiguous semidirect product	C₄₁⋊(C₁₃×C₂₅)
unambiguous semidirect product	(C₁₃×C₄₁)⋊C₂₅

Splittings

derived, Sylow	C₄₁ ⋊ C₁₃×C₂₅
Hall	C₁₃×C₄₁ ⋊ C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₁₃	C₄₁⋊C₅
commutator, hypocenter	C₄₁	C₁₃×C₂₅
Frattini	C₅	C₁₃×C₄₁⋊C₅
Fitting, socle, prime radical	C₅×C₁₃×C₄₁	C₅
cosocle	C₅×C₄₁	C₅×C₁₃
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₅×C₁₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 13325

A minimal faithful permutation representation — 2 generators on 79 points:

(2,3,5,9,17)(4,7,13,24,35)(6,11,20,12,22)(8,15,23,34,21)(10,19,30,18,29)(14,25,36,40,33)(16,28,27,38,41)(26,37,31,39,32)(42,43,45,48,52,44,46,49,53,57,47,50,54,58,61,51,55,59,62,64,56,60,63,65,66)(67,68,69,70,71,72,73,74,75,76,77,78,79);(1,2,4,8,16,25,29,34,40,36,3,6,12,23,30,37,9,18,5,10,7,14,26,38,39,41,19,31,11,21,15,27,24,35,20,32,13,17,22,33,28)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₃×C₄₁⋊C₂₅, C₁₃×D₄₁⋊C₂₅, D₁₃×C₄₁⋊C₂₅, …
maximal normal subgroup of	C₂×C₁₃×C₄₁⋊C₂₅, C₁₃×D₄₁⋊C₂₅, D₁₃×C₄₁⋊C₂₅, …
maximal quotient of	C₂×C₁₃×C₄₁⋊C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13325, 2);

C13×C41⋊C25 #27211017