C₃×C₂₅×D₈₇ #27189382

order	13050
isoclinism	isoclinic class of D₈₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₂₅×D₈₇
unambiguous semidirect product	C₃⋊(C₃×C₂₅×D₂₉)
unambiguous semidirect product	C₂₉⋊(C₃×D₃×C₂₅)

Splittings

Fitting, Hall	C₃²×C₂₅×C₂₉ ⋊ C₂
derived	C₃×C₂₉ ⋊ C₂×C₃×C₂₅
Hall	C₂₅×C₂₉ ⋊ C₃×D₃
Hall	C₃²×C₂₉ ⋊ C₂×C₂₅
Hall	C₃²×C₂₅ ⋊ D₂₉
Sylow	C₂₉ ⋊ C₃×D₃×C₂₅
Sylow	C₃² ⋊ C₂₅×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₅	D₈₇
commutator, hypocenter	C₃×C₂₉	C₂×C₃×C₂₅
Frattini	C₅	C₃×C₅×D₈₇
Fitting	C₃²×C₂₅×C₂₉	C₂
socle	C₃²×C₅×C₂₉	C₂×C₅
prime radical	C₃×C₅×D₈₇	C₅
cosocle	C₃×C₅×C₂₉	C₂×C₃×C₅
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₃×C₂₅

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 4350

A minimal faithful permutation representation — 2 generators on 60 points:

(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)(34,35)(36,40,48,56,60,38,44,53,59,46,41,49,57,42,51,45,54,39,47,55,50,37,43,52,58);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(33,34,35)

Conjugacy classes & character table

3375 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₃×C₂₅×D₂₉, C₃×D₂₅×D₈₇, C₃×D₇₅⋊D₂₉, …
maximal normal subgroup of	C₃×D₃×C₂₅×D₂₉, C₃×D₂₅×D₈₇, C₃×D₇₅⋊D₂₉, …
maximal quotient of	C₃×C₂₅×Dic₈₇, C₂×C₃×C₂₅×D₈₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13050, 14);

C3×C25×D87 #27189382