C₇×#63256 #14274162

order	1904
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂²

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₇×#63256

Splittings

Fitting	C₇×Q₈×C₁₇ ⋊ C₂
Hall	C₇×C₁₇ ⋊ #41
Sylow	C₁₇ ⋊ C₇×#41

Subgroups

	subgroup	G/H
center	C₂×C₇	C₂²×D₁₇
commutator, cosocle	C₂×C₁₇	C₂³×C₇
Frattini	C₂	C₂²×C₇×D₁₇
Fitting	C₇×Q₈×C₁₇	C₂
socle	C₂×C₇×C₁₇	C₂³
hypercenter	C₇×Q₈	D₁₇
hypocenter	C₁₇	C₇×#41
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₇ ◁ C₇×Q₈

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 952

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5,6,7)(8,9,11,13,15,17,19,21,23,24,22,20,18,16,14,12,10)(25,27,28,31)(26,29,30,32);(25,26,28,30)(27,32,31,29);(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(27,31)(29,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1904, 145);

C7×#63256 #14274162