C₅×#67273 #14270261

order	1840
isoclinism	isoclinic class of #67272
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×#67273

Splittings

Hall	C₅×C₂₃ ⋊ SD₁₆
Sylow	C₂₃ ⋊ C₅×SD₁₆

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂²⋊D₂₃
commutator, cosocle	C₄×C₂₃	C₂²×C₅
Frattini	C₄	C₂×C₅×D₂₃
Fitting, prime radical	C₅×D₄×C₂₃	C₂
socle	C₂×C₅×C₂₃	D₄
hypercenter	C₅×D₄	D₂₃
hypocenter	C₂₃	C₅×SD₁₆
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×D₄

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 920

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3,4,5)(6,7,9,11,13,15,17,19,21,23,25,27,28,26,24,22,20,18,16,14,12,10,8)(30,33)(31,36)(34,35);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30,32,35)(31,33,36,34)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1840, 44);

C5×#67273 #14270261