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C₂²×#1039 #87905

order	400
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³×C₅

Aliases

Splittings

C₅² ⋊ C₂²×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂³	C₅⋊D₅
commutator, hypocenter	C₅²	C₂²×C₄
Frattini	C₂	C₂²×C₅⋊D₅
Fitting, socle, prime radical	C₂³×C₅²	C₂
cosocle	C₂×C₅²	C₂³
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂³

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 400

A minimal faithful permutation representation — 3 generators on 18 points:

(1,2)(3,4)(5,6,7,8)(10,11)(12,13)(15,16)(17,18);(3,4)(9,10,12,13,11);(1,2)(14,15,17,18,16)

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716620, #11716698, C₂²⋊#6033, …
maximal normal subgroup of	#11716620, #11716698, C₂²⋊#6033, …
maximal quotient of	C₂²×#6029, C₂×#87804, C₂×C₄×#1039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 199);