C₁₇×#4294 #15668554

order	2907
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₇×#4294

Splittings

derived, Sylow	C₁₉ ⋊ C₉×C₁₇
Hall	C₁₇×C₁₉ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₉×C₁₇
Frattini	C₃	C₁₇×C₁₉⋊C₃
Fitting, socle, prime radical	C₃×C₁₇×C₁₉	C₃
cosocle	C₃×C₁₉	C₃×C₁₇
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₁₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 2907

A minimal faithful permutation representation — 2 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20,22)(21,24,25)(23,27,26)(28,32,30)(29,33,31)(34,36,35)(37,38,40,39,41,43,42,44,45);(18,19,21,25,30,35,32,20,23,28,33,22,26,31,24,29,34,36,27)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₇×C₂²⋊#4294, C₅×C₁₇×#4294, C₇×C₁₇×#4294, …
maximal normal subgroup of	C₅×C₁₇×#4294, C₇×C₁₇×#4294, C₁₁×C₁₇×#4294, …
maximal quotient of	C₁₇×C₂²⋊#4294, C₅×C₁₇×#4294, C₇×C₁₇×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2907, 2);

C17×#4294 #15668554