C₃×C₂₉×D₂₅ #16864731

order	4350
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₂₉×D₂₅
unambiguous semidirect product	C₂₅⋊(C₂×C₃×C₂₉)

Splittings

Fitting, Hall	C₃×C₂₅×C₂₉ ⋊ C₂
derived, Sylow	C₂₅ ⋊ C₂×C₃×C₂₉
Hall	C₂₅×C₂₉ ⋊ C₂×C₃
Hall	C₃×C₂₅ ⋊ C₂×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₉	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₃×C₂₉
Frattini	C₅	C₃×D₅×C₂₉
Fitting	C₃×C₂₅×C₂₉	C₂
socle	C₃×C₅×C₂₉	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃×C₂₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2175

A minimal faithful permutation representation — 2 generators on 57 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57);(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₂₉×D₂₅, C₃²×C₂₉×D₂₅, C₃×C₂₉×D₇₅, …
maximal normal subgroup of	C₉×C₂₉×D₂₅, C₃²×C₂₉×D₂₅, C₃×C₇×C₂₉×D₂₅, …
maximal quotient of	C₉×C₂₉×D₂₅, C₃²×C₂₉×D₂₅, C₃×C₂₉×D₇₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4350, 3);

C3×C29×D25 #16864731