C₅×#4873 #11750372

order	960
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#4873

Splittings

Hall	C₃×C₅ ⋊ C₄×Q₁₆
Sylow	C₃ ⋊ C₄×C₅×Q₁₆

Subgroups

	subgroup	G/H
center	C₂²×C₅	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#107	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×D₄
cosocle	C₂×C₃×C₄	C₂³×C₅
hypercenter	C₅×#107	D₃
hypocenter	C₃	C₄×C₅×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#107

220 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 28
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#69337, C₅×#69175, #14315398, …
maximal normal subgroup of	C₅×#69337, C₅×#69175, #14315398, …
maximal quotient of	C₅×#68557, C₅×#68560, C₅×#68564, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4567);