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#44416552

order	29248
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Splittings

C₄₅₇ ⋊ #346

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₄₅₇
commutator	C₂×C₄₅₇	C₄×C₈
Fitting	C₂×C₁₆×C₄₅₇	C₂
socle, prime radical	C₂²×C₄₅₇	C₂×C₈
cosocle	C₂×C₈×C₄₅₇	C₂²
hypercenter	C₂×C₁₆	D₄₅₇
hypocenter	C₄₅₇	#346
LCS	G ▷ C₂×C₄₅₇ ▷ C₄₅₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 29248

Polycyclic presentation:

2^6,457|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^b=g^456

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, 324);