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D₄×C₅⋊D₅ #87901

order	400
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₅

Aliases

D₄×C₅⋊D₅

Splittings

Fitting	C₅²×D₄ ⋊ C₂
Sylow	C₅² ⋊ C₂×D₄

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂²×C₅⋊D₅
commutator, socle, cosocle	C₂×C₅²	C₂³
Fitting	C₅²×D₄	C₂
hypercenter	D₄	C₅⋊D₅
hypocenter	C₅²	C₂×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ D₄

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 100

A minimal faithful permutation representation — 3 generators on 14 points:

(6,7)(8,9)(11,12)(13,14);(2,4)(10,11,13,14,12);(1,2)(3,4)(5,6,8,9,7)

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716875, #11716900, #11717044, …
maximal normal subgroup of	#11716875, #11716900, #11717044, …
maximal quotient of	#11717198, C₂²⋊C₄×C₅⋊D₅, #11717201, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 195);