Finite Group Databasebeta

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C₂²⋊Q₈×#1043 #72221163

order	3200
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂²⋊Q₈×#1043

Splittings

Fitting	C₅²×C₂²⋊Q₈ ⋊ C₄
Sylow	C₅² ⋊ C₄×C₂²⋊Q₈

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂³×#1043
commutator, socle	C₂²×C₅²	C₂³×C₄
Fitting	C₅²×C₂²⋊Q₈	C₄
prime radical	C₂³×C₅⋊D₅	C₂³
cosocle	C₂²×C₅⋊D₅	C₂⁴
hypercenter	C₂²⋊Q₈	#1043
hypocenter	C₅²	C₄×C₂²⋊Q₈
LCS	G ▷ C₂²×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

2624 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#525×#1043
maximal normal subgroup of	#525×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.