C₇×D₁₆₅ #14556333

order	2310
isoclinism	isoclinic class of D₁₆₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₁₆₅
unambiguous semidirect product	C₃⋊(C₇×D₅₅)
unambiguous semidirect product	C₅⋊(C₇×D₃₃)
unambiguous semidirect product	C₁₁⋊(C₇×D₁₅)

	subgroup	G/H
center, hypercenter	C₇	D₁₆₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₁	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₁	C₂
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₇

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1155

A minimal faithful permutation representation — 2 generators on 26 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);(9,10)(12,15)(13,14)(17,26)(18,25)(19,24)(20,23)(21,22)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2310, 17);