#37509154

order	22912
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₇₉ ⋊ #1843

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₇₉
commutator, socle, prime radical	C₂³×C₁₇₉	C₂²×C₄
Fitting	#376×C₁₇₉	C₂
cosocle	C₂²×C₄×C₁₇₉	C₂³
hypercenter	#376	D₁₇₉
hypocenter	C₁₇₉	#1843
LCS	G ▷ C₂³×C₁₇₉ ▷ C₁₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

256 conjugacy classes of subgroups.

μ_t(G) = 22912

Polycyclic presentation:

2^7,179|a^2=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^178,c^b=cg

3604 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22912, 4664);