#87721

order	400
isoclinism	isoclinic class of #87721
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Sylow

C₂₅ ⋊ SD₁₆

Subgroups

	subgroup	G/H
center	C₂	C₂²⋊D₂₅
commutator, cosocle	C₄×C₂₅	C₂²
Frattini	C₄×C₅	C₂×D₅
Fitting	D₄×C₂₅	C₂
socle	C₂×C₅	C₂²⋊D₅
prime radical	C₅×D₄	D₅
hypercenter	D₄	D₂₅
hypocenter	C₂₅	SD₁₆
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 200

A minimal faithful permutation representation — 2 generators on 33 points:

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

Polycyclic presentation:

2^4,5^2|a^2=d,c^2=d,e^5=f^4,b^a=bc,c^a=cd,e^a=e^4f,f^a=f^4,c^b=cd

Conjugacy classes & character table

67 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716473, #11716474, SD₁₆×D₂₅, …
maximal normal subgroup of	#11716473, #11716474, SD₁₆×D₂₅, …
maximal quotient of	#11716356, #11716357, #11716381, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 15);