C₂×C₂₃×D₁₄₇ #27214099

order	13524
isoclinism	isoclinic class of D₁₄₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₂₃×D₁₄₇
unambiguous semidirect product	(C₂×C₃)⋊(C₂₃×D₄₉)
unambiguous semidirect product	(C₂×C₄₉)⋊(D₃×C₂₃)

Splittings

Fitting	C₂×C₃×C₂₃×C₄₉ ⋊ C₂
derived, Hall	C₃×C₄₉ ⋊ C₂²×C₂₃
Hall	C₃×C₂₃×C₄₉ ⋊ C₂²
Hall	C₂₃×C₄₉ ⋊ C₂×D₃
Hall	C₃×C₂₃ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×D₃×C₂₃
Sylow	C₃ ⋊ C₂×C₂₃×D₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₃	D₁₄₇
commutator, cosocle, hypocenter	C₃×C₄₉	C₂²×C₂₃
Frattini	C₇	C₂×C₂₃×D₂₁
Fitting	C₂×C₃×C₂₃×C₄₉	C₂
socle	C₂×C₃×C₇×C₂₃	D₇
LCS	G ▷ C₃×C₄₉
UCS	C₁ ◁ C₂×C₂₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 6762

A minimal faithful permutation representation — 2 generators on 77 points:

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

Conjugacy classes & character table

3450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13524, 33);

C2×C23×D147 #27214099