#44484692

order	30592
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

C₂₃₉ ⋊ #1840

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₃₉
commutator, socle, prime radical	C₂³×C₂₃₉	C₂²×C₄
Fitting	#336×C₂₃₉	C₂
cosocle	C₂²×C₄×C₂₃₉	C₂³
hypercenter	#336	D₂₃₉
hypocenter	C₂₃₉	#1840
LCS	G ▷ C₂³×C₂₃₉ ▷ C₂₃₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

196 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

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

μ_t(G) = 30592

Polycyclic presentation:

2^7,239|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^c=h^238

4804 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 4654);