C₃×C₅×Dic₄₇ #15667686

order	2820
isoclinism	isoclinic class of D₄₇
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₅×Dic₄₇
unambiguous semidirect product	C₄₇⋊(C₃×C₄×C₅)

Splittings

derived, Sylow	C₄₇ ⋊ C₃×C₄×C₅
Hall	C₃×C₅×C₄₇ ⋊ C₄
Hall	C₅×C₄₇ ⋊ C₃×C₄
Hall	C₃×C₄₇ ⋊ C₄×C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₄₇
commutator, hypocenter	C₄₇	C₃×C₄×C₅
Frattini	C₂	C₃×C₅×D₄₇
Fitting, socle, prime radical	C₂×C₃×C₅×C₄₇	C₂
cosocle	C₂×C₄₇	C₂×C₃×C₅
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂×C₃×C₅

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 2820

A minimal faithful permutation representation — 2 generators on 59 points:

(1,2,3)(4,5,6,7,8)(9,10)(11,12)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59);(9,11,10,12)(14,59)(15,58)(16,57)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₂₅×Dic₄₇, C₃×C₅²×Dic₄₇, C₃×C₅×Dic₂₃₅, …
maximal normal subgroup of	C₃×C₂₅×Dic₄₇, C₃×C₅²×Dic₄₇, C₃×C₅×C₇×Dic₄₇, …
maximal quotient of	C₃×C₂₅×Dic₄₇, C₃×C₅²×Dic₄₇, C₃×C₅×Dic₂₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2820, 2);

C3×C5×Dic47 #15667686