C₉×#3956 #13083785

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₉×#3956

Splittings

Hall	C₅×C₉ ⋊ #101
Sylow	C₅ ⋊ C₉×#101

Subgroups

	subgroup	G/H
center	C₂×C₉	#685
commutator	C₂²×C₅	C₂×C₄×C₉
Frattini	C₂×C₃×C₄	C₂×C₃×D₅
Fitting	C₅×C₉×M₁₆	C₂
socle	C₂×C₃×C₅	C₃×C₂²⋊C₄
prime radical	C₂²×C₃×C₅	C₂×C₃×C₄
cosocle	C₂×C₃×C₄×C₅	C₂²×C₃
hypercenter	C₉×M₁₆	D₅
hypocenter	C₅	C₉×#101
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₉×M₁₆

114 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 102);