C₇×#6107 #13089792

order	1456
isoclinism	isoclinic class of #6104
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇×#6107

Splittings

Hall	C₇×C₁₃ ⋊ Q₁₆
Sylow	C₁₃ ⋊ C₇×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₇	C₂²⋊D₁₃
commutator, cosocle	C₄×C₁₃	C₂²×C₇
Frattini	C₄	C₂×C₇×D₁₃
Fitting	C₇×Q₈×C₁₃	C₂
socle, prime radical	C₂×C₇×C₁₃	D₄
hypercenter	C₇×Q₈	D₁₃
hypocenter	C₁₃	C₇×Q₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₇ ◁ C₄×C₇ ◁ C₇×Q₈

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1456

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3,4,5,6,7)(8,9,11,13,15,17,19,20,18,16,14,12,10)(21,23,25,31)(22,26,28,35)(24,33,34,30)(27,36,32,29);(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22,25,28)(23,29,31,36)(24,32,34,27)(26,33,35,30)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1456, 46);

C7×#6107 #13089792