C₂₉×D₂₅ #13089691

order	1450
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×D₂₅
unambiguous semidirect product	C₂₅⋊(C₂×C₂₉)

Splittings

Fitting, Hall	C₂₅×C₂₉ ⋊ C₂
derived, Sylow	C₂₅ ⋊ C₂×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₂₉
Frattini	C₅	D₅×C₂₉
Fitting	C₂₅×C₂₉	C₂
socle	C₅×C₂₉	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 725

A minimal faithful permutation representation — 2 generators on 54 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)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54);(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#1035, #15668504, D₂₅×D₂₉, …
maximal normal subgroup of	C₂₉×#1035, #15668504, D₂₅×D₂₉, …
maximal quotient of	C₂₉×Dic₂₅, C₂×C₂₉×D₂₅, C₃×C₂₉×D₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1450, 1);

C29×D25 #13089691