#87724

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

Aliases

No aliases for this group.

Splittings

Fitting	Q₈×C₂₅ ⋊ C₂
Sylow	C₂₅ ⋊ SD₁₆

Subgroups

	subgroup	G/H
center	C₂	C₂²⋊D₂₅
commutator, cosocle	C₄×C₂₅	C₂²
Frattini	C₄×C₅	C₂×D₅
Fitting	Q₈×C₂₅	C₂
socle	C₂×C₅	C₂²⋊D₅
prime radical	D₁₀₀	C₂
hypercenter	Q₈	D₂₅
hypocenter	C₂₅	SD₁₆
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

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

Polycyclic presentation:

2^4,5^2|b^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	SD₁₆×D₂₅, #11716476, #11716480, …
maximal normal subgroup of	SD₁₆×D₂₅, #11716476, #11716480, …
maximal quotient of	#11716356, #11716358, #11716384, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 18);