C₂₉×#216 #13063552

order	1392
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂₉×#216

Splittings

Hall	C₃×C₂₉ ⋊ Q₁₆
Sylow	C₃ ⋊ Q₁₆×C₂₉

Subgroups

	subgroup	G/H
center	C₂×C₂₉	#67
commutator, cosocle	C₃×C₄	C₂²×C₂₉
Frattini	C₄	C₂×D₃×C₂₉
Fitting	C₃×Q₈×C₂₉	C₂
socle, prime radical	C₂×C₃×C₂₉	D₄
hypercenter	Q₈×C₂₉	D₃
hypocenter	C₃	Q₁₆×C₂₉
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₂₉ ◁ C₄×C₂₉ ◁ Q₈×C₂₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 1392

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1392, 63);

C29×#216 #13063552