#38735151

order	24896
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₃₈₉ ⋊ #446

	subgroup	G/H
center, Frattini	C₂²	C₂²×#13095555
commutator, socle, prime radical	C₂²×C₃₈₉	C₂²×C₄
Fitting	C₄⋊C₄×C₃₈₉	C₄
cosocle	C₂×Dic₃₈₉	C₂³
hypercenter	C₄⋊C₄	#13095555
hypocenter	C₃₈₉	#446
LCS	G ▷ C₂²×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

94 conjugacy classes of subgroups.

μ_t(G) = 24896

Polycyclic presentation:

2^6,389|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^274,g^b=g^388,g^c=g^115,g^e=g^388

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 1601);