Finite Group Databasebeta

← Prev (#27135110) Next (#27135112) →

C₄×C₄⋊Dic₁₉₃ #27135111

order	12352
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₄×C₄⋊Dic₁₉₃

Splittings

C₁₉₃ ⋊ C₄×C₄⋊C₄

Subgroups

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

194 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, 401);