Finite Group Databasebeta

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C₂×C₄⋊#13095393 #27135280

order	12352
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₄⋊#13095393

Splittings

C₁₉₃ ⋊ C₂×C₄⋊C₈

Subgroups

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₉₃
commutator	C₂×C₁₉₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₁₉₃
Fitting	C₂×C₄²×C₁₉₃	C₂
socle, prime radical	C₂³×C₁₉₃	C₂×C₄
cosocle	C₂×C₄×C₁₉₃	C₂³
hypercenter	C₂×C₄²	D₁₉₃
hypocenter	C₁₉₃	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

138 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 570);