C₈×D₂₅ #87711

order	400
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₈×D₂₅

Splittings

Fitting	C₈×C₂₅ ⋊ C₂
derived, Sylow	C₂₅ ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₈	D₂₅
commutator, hypocenter	C₂₅	C₂×C₈
Frattini	C₄×C₅	C₂×D₅
Fitting	C₈×C₂₅	C₂
socle	C₂×C₅	C₄×D₅
prime radical	C₂×D₂₅	C₄
cosocle	C₄×C₂₅	C₂²
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₈

33 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:

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₆×D₂₅, #11716346, D₂₅⋊C₁₆, …
maximal normal subgroup of	C₁₆×D₂₅, #11716346, D₂₅⋊C₁₆, …
maximal quotient of	C₁₆×D₂₅, #11716346, C₈×Dic₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 5);

C8×D25 #87711

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₈×D₂₅ #87711