C₅×D₂₃₁ #14556331

order	2310
isoclinism	isoclinic class of D₂₃₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₂₃₁
unambiguous semidirect product	C₃⋊(C₅×D₇₇)
unambiguous semidirect product	C₇⋊(C₅×D₃₃)

	subgroup	G/H
center, hypercenter	C₅	D₂₃₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₁	C₂
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₅

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);(7,8)(10,15)(11,14)(12,13)(17,26)(18,25)(19,24)(20,23)(21,22)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2310, 15);