D₇×C₈₃ #11923960

order	1162
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₈₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇×C₈₃
unambiguous semidirect product	C₇⋊(C₂×C₈₃)

Splittings

Fitting, socle, Hall	C₇×C₈₃ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₈₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₈₃
Frattini	C₁	G
Fitting, socle	C₇×C₈₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₈₃

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 90
transitive degree	μ_t(G) = 581

A minimal faithful permutation representation — 2 generators on 90 points:

(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90);(2,7)(3,6)(4,5)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₇×D₈₃, C₂×D₇×C₈₃, C₃×D₇×C₈₃, …
maximal normal subgroup of	D₇×D₈₃, C₂×D₇×C₈₃, C₃×D₇×C₈₃, …
maximal quotient of	Dic₇×C₈₃, C₂×D₇×C₈₃, C₃×D₇×C₈₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1162, 1);

D7×C83 #11923960