C₇×Dic₄₄ #11927651

order	1232
isoclinism	isoclinic class of #4314
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇×Dic₄₄

Splittings

Hall	C₇×C₁₁ ⋊ Q₁₆
Sylow	C₁₁ ⋊ C₇×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₇	D₄₄
commutator, cosocle	C₄×C₁₁	C₂²×C₇
Frattini	C₄	C₂×C₇×D₁₁
Fitting	C₇×C₈×C₁₁	C₂
socle, prime radical	C₂×C₇×C₁₁	D₄
hypercenter	C₇×C₈	D₁₁
hypocenter	C₁₁	C₇×Q₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₇ ◁ C₄×C₇ ◁ C₇×C₈

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 1232

A minimal faithful permutation representation — 2 generators on 34 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1232, 34);

C7×Dic44 #11927651