Finite Group Databasebeta

← Prev (#44537881) Next (#44537883) →

#44537882

order	31456
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Splittings

C₉₈₃ ⋊ #101

Subgroups

	subgroup	G/H
center	C₂	C₂²⋊Dic₉₈₃
commutator, prime radical	C₂²×C₉₈₃	C₂×C₄
Frattini	C₂×C₄	C₂×D₉₈₃
Fitting	C₂×Q₈×C₉₈₃	C₂
socle	C₂×C₉₈₃	C₂²⋊C₄
cosocle	C₂×C₄×C₉₈₃	C₂²
hypercenter	C₂×Q₈	D₉₈₃
hypocenter	C₉₈₃	#101
LCS	G ▷ C₂²×C₉₈₃ ▷ C₂×C₉₈₃ ▷ C₉₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15728

Polycyclic presentation:

2^5,983|a^2=d,b^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^982,d^b=de

Conjugacy classes & character table

4921 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31456, 65);