#26021193

order	11392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₈₉ ⋊ #1985

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂²×C₄
Fitting	C₂×C₄×Q₈×C₈₉	C₂
cosocle	C₂²×C₄×C₈₉	C₂³
hypercenter	C₂×C₄×Q₈	D₈₉
hypocenter	C₈₉	#1985
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×Q₈

280 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Polycyclic presentation:

2^7,89|a^2=f,b^2=def,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^88,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, 5451);