#90784

order	464
isoclinism	isoclinic class of #90782
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting	Q₈×C₂₉ ⋊ C₂
Sylow	C₂₉ ⋊ SD₁₆

Subgroups

	subgroup	G/H
center	C₂	C₂²⋊D₂₉
commutator, cosocle	C₄×C₂₉	C₂²
Frattini	C₄	C₂×D₂₉
Fitting	Q₈×C₂₉	C₂
socle	C₂×C₂₉	D₄
prime radical	D₁₁₆	C₂
hypercenter	Q₈	D₂₉
hypocenter	C₂₉	SD₁₆
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 232

A minimal faithful permutation representation — 2 generators on 37 points:

(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)(30,31,33,35)(32,37,36,34);(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)(31,34)(32,36)(35,37)

Polycyclic presentation:

2^4,29|b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^28,c^b=cd

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SD₁₆×D₂₉, #11745276, #11745280, …
maximal normal subgroup of	SD₁₆×D₂₉, #11745276, #11745280, …
maximal quotient of	#11745156, #11745157, #11745183, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 17);