C₅×#70915 #14317254

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#70915

Splittings

Fitting	C₃×C₄×C₅×Q₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ #2211
Sylow	C₃ ⋊ C₅×#2211

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂×#213
commutator, cosocle	C₂×C₃×C₈	C₂³×C₅
Frattini	C₂×C₈	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂×D₈
prime radical	C₂×C₅×D₂₄	C₂²
hypercenter	C₄×C₅×Q₁₆	D₃
hypocenter	C₃	C₅×#2211
LCS	G ▷ C₂×C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×C₈ ◁ C₄×C₅×Q₁₆

316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 44 points:

(1,2,3,4,5)(6,7,8)(13,15,16,24)(14,20,19,34)(17,30,27,44)(18,33,28,26)(21,37,35,43)(22,38,32,36)(23,40,39,29)(25,42,41,31);(9,10,11,12)(14,19)(20,34)(21,35)(22,32)(23,39)(29,40)(36,38)(37,43);(7,8)(10,12)(13,14)(15,23)(16,19)(17,29)(18,32)(20,25)(21,31)(22,28)(24,39)(26,43)(27,40)(30,38)(33,37)(34,41)(35,42)(36,44)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 42952);

C5×#70915 #14317254