C₈×D₂₉ #90771

order	464
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₈×D₂₉

Splittings

Fitting	C₈×C₂₉ ⋊ C₂
derived, Sylow	C₂₉ ⋊ C₂×C₈

Subgroups

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

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:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₆×D₂₉, #11745146, D₂₉⋊C₁₆, …
maximal normal subgroup of	C₁₆×D₂₉, #11745146, D₂₉⋊C₁₆, …
maximal quotient of	C₁₆×D₂₉, #11745146, C₈×Dic₂₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 4);

C8×D29 #90771

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₈×D₂₉ #90771