Finite Group Databasebeta

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C₄×C₄⋊Dic₄₅₇ #44416629

order	29248
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₄×C₄⋊Dic₄₅₇

Splittings

C₄₅₇ ⋊ C₄×C₄⋊C₄

Subgroups

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₅₇
commutator	C₂×C₄₅₇	C₂×C₄²
Frattini	C₂³	C₂²×D₄₅₇
Fitting	C₂×C₄²×C₄₅₇	C₂
socle, prime radical, cosocle	C₂³×C₄₅₇	C₂³
hypercenter	C₂×C₄²	D₄₅₇
hypocenter	C₄₅₇	C₄×C₄⋊C₄
LCS	G ▷ C₂×C₄₅₇ ▷ C₄₅₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 29248

Conjugacy classes & character table

7336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 401);