#37588478

order	24512
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₃₈₃ ⋊ #446

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₈₃
commutator, socle, prime radical	C₂²×C₃₈₃	C₂²×C₄
Fitting	C₄⋊C₈×C₃₈₃	C₂
cosocle	C₂×C₄×C₃₈₃	C₂³
hypercenter	C₄⋊C₈	D₃₈₃
hypocenter	C₃₈₃	#446
LCS	G ▷ C₂²×C₃₈₃ ▷ C₃₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

94 conjugacy classes of subgroups.

μ_t(G) = 24512

Polycyclic presentation:

2^6,383|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^c=g^382

3848 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24512, 676);