C₇×D₉₂ #13046232

order	1288
isoclinism	isoclinic class of Dic₄₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

metacyclic
supersolvable
metabelian
solvable
monomial

Aliases

direct product	C₇×D₉₂
unambiguous semidirect product	C₄⋊(C₇×D₂₃)

Splittings

Fitting	C₄×C₇×C₂₃ ⋊ C₂
Hall	C₇×C₂₃ ⋊ D₄
Sylow	C₂₃ ⋊ C₇×D₄

Subgroups

	subgroup	G/H
center	C₂×C₇	C₂×D₂₃
commutator, cosocle	C₂×C₂₃	C₂²×C₇
Frattini	C₂	C₂×C₇×D₂₃
Fitting	C₄×C₇×C₂₃	C₂
socle	C₂×C₇×C₂₃	C₂²
hypercenter	C₄×C₇	D₂₃
hypocenter	C₂₃	C₇×D₄
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₇ ◁ C₄×C₇

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 644

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1288, 14);

C7×D92 #13046232