D₂₅⋊C₈ #87734

order	400
isoclinism	isoclinic class of #1035
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product

D₂₅⋊C₈

Splittings

derived, Sylow

C₂₅ ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₄	#1035
commutator, hypocenter	C₂₅	C₂×C₈
Frattini, socle	C₂×C₅	C₂×AGL(1,𝔽₅)
Fitting	C₄×C₂₅	C₄
prime radical	C₂×D₂₅	C₄
cosocle	Dic₂₅	C₂²
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₄

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:

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

Polycyclic presentation:

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

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₈×#1035, #11716410, #11716424, …
maximal normal subgroup of	C₈×#1035, #11716410, #11716424, …
maximal quotient of	D₂₅⋊C₁₆, #11716406, C₄×#6016, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 28);

D25⋊C8 #87734