Finite Group Databasebeta

← Prev (#44537872) Next (#44537874) →

#44537873

order	31456
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Splittings

C₉₈₃ ⋊ #97

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₉₈₃
commutator	C₂×C₉₈₃	C₄²
Fitting	C₂×C₈×C₉₈₃	C₂
socle, prime radical	C₂²×C₉₈₃	C₂×C₄
cosocle	C₂×C₄×C₉₈₃	C₂²
hypercenter	C₂×C₈	D₉₈₃
hypocenter	C₉₈₃	#97
LCS	G ▷ C₂×C₉₈₃ ▷ C₉₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 31456

Polycyclic presentation:

2^5,983|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^982

Conjugacy classes & character table

7876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31456, 56);