C₅×#63359 #13083801

order	1440
isoclinism	isoclinic class of D₁₄₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×#63359

Splittings

Fitting	C₅×C₉×C₁₆ ⋊ C₂
Hall	C₅×C₉ ⋊ SD₃₂
Sylow	C₉ ⋊ C₅×SD₃₂

Subgroups

	subgroup	G/H
center	C₂×C₅	D₇₂
commutator, cosocle	C₈×C₉	C₂²×C₅
Frattini	C₃×C₈	C₂×C₅×D₃
Fitting	C₅×C₉×C₁₆	C₂
socle	C₂×C₃×C₅	D₂₄
prime radical	C₅×D₇₂	C₂
hypercenter	C₅×C₁₆	D₉
hypocenter	C₉	C₅×SD₃₂
LCS	G ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 30 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 118);

C5×#63359 #13083801