D₂₉⋊C₈ #90795

order	464
isoclinism	isoclinic class of #1181
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product

D₂₉⋊C₈

Splittings

derived, Sylow

C₂₉ ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₄	#1181
commutator, hypocenter	C₂₉	C₂×C₈
Frattini	C₂	C₂×#1181
Fitting	C₄×C₂₉	C₄
socle	C₂×C₂₉	C₂×C₄
prime radical	C₂×D₂₉	C₄
cosocle	Dic₂₉	C₂²
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₄

22 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:

(1,2,5,10,19,15,23,17,26,28,24,12,3,7,14,22,13,6,11,20,27,29,25,21,8,16,18,9,4)(30,32,34,33)(31,35,37,36);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,25)(14,21,22,23)(16,24,19,20)(26,28,29,27)(30,31,33,36,34,37,32,35)

Polycyclic presentation:

2^4,29|a^2=c,b^2=d,c^2=d,e^a=e^12,e^c=e^28

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₈×#1181, #11745208, #11745223, …
maximal normal subgroup of	C₈×#1181, #11745208, #11745223, …
maximal quotient of	D₂₉⋊C₁₆, #11745206, C₄×#6599, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 28);

D29⋊C8 #90795