Finite Group Databasebeta

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C₂×#72242230 #72253261

order	6400
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴

Aliases

C₂×#72242230

Splittings

Fitting	C₂×C₅²×#108 ⋊ C₄
Sylow	C₅² ⋊ C₂×#1383

Subgroups

	subgroup	G/H
center	C₂²	#13100253
commutator	C₅²×C₈	C₂×C₄²
Frattini	C₂×C₈	C₂²×#1043
Fitting	C₂×C₅²×#108	C₄
socle	C₂²×C₅²	#340
prime radical	C₂³×C₅⋊D₅	SD₁₆
cosocle	C₂×C₈×C₅⋊D₅	C₂³
hypercenter	C₂×#108	#1043
hypocenter	C₅²	C₂×#1383
LCS	G ▷ C₅²×C₈ ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

2456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 800

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#365×#1043
maximal normal subgroup of	C₂×#365×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.