#13390455

order	1792
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Splittings

Sylow

C₇ ⋊ #24349

Subgroups

	subgroup	G/H
center	C₂³	C₂×D₄×D₇
commutator, cosocle	C₂²×C₄×C₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇
Fitting	C₇×#1862	C₂
socle	C₂³×C₇	C₂²×D₄
prime radical	C₂²×C₇×D₄	C₂³
hypercenter	#1862	D₇
hypocenter	C₇	#24349
LCS	G ▷ C₂²×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1862

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 896

Polycyclic presentation:

2^8,7|a^2=e,b^2=eh,c^2=h,d^2=eh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,g^a=gh,i^a=i^6,c^b=cg,f^b=fh,g^b=gh,i^b=i^6,d^c=dh,f^c=fh,g^c=gh,i^c=i^6,i^d=i^6

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 206227);