C₂²⋊Dic₂₉ #90786

order	464
isoclinism	isoclinic class of Dic₅₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

unambiguous semidirect product

C₂²⋊Dic₂₉

Splittings

Sylow

C₂₉ ⋊ C₂²⋊C₄

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂×D₂₉
commutator	C₂×C₂₉	C₂×C₄
Fitting, prime radical	C₂³×C₂₉	C₂
socle, cosocle	C₂²×C₂₉	C₂²
hypercenter	C₂³	D₂₉
hypocenter	C₂₉	C₂²⋊C₄
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂³

34 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)(35,37);(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)(34,35)(36,37)

Polycyclic presentation:

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

Conjugacy classes & character table

122 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11745154, #11745182, #11745239, …
maximal normal subgroup of	#11745154, #11745182, #11745239, …
maximal quotient of	C₂²⋊#6597, #11745179, #11745180, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 19);

C22⋊Dic29 #90786