#26023559

order	11392
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₈₉ ⋊ #2402

	subgroup	G/H
center	C₂²×C₄	C₂²×D₈₉
commutator, socle, prime radical, cosocle	C₂³×C₈₉	C₂⁴
Frattini	C₂³	C₂³×D₈₉
Fitting	C₄×C₄⋊C₄×C₈₉	C₂
hypercenter	C₄×C₄⋊C₄	D₈₉
hypocenter	C₈₉	#2402
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

400 conjugacy classes of subgroups.

Polycyclic presentation:

2^7,89|a^2=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^88

1804 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 7817);