C₁₇×#2194 #14525200

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2192
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2194

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#447
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₁₇×#576	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#131 ◁ G

216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,24,30)(20,31,34,47)(21,35,39,46)(22,29,23,28)(25,41,44,32)(26,40,45,33)(27,37,42,38)(36,48,49,43);(18,20)(19,25)(21,36)(22,33)(23,40)(24,34)(26,42)(27,45)(28,43)(29,48)(30,44)(31,35)(32,38)(37,41)(39,49)(46,47);(18,20)(19,26)(21,32)(22,40)(23,33)(24,34)(25,42)(27,44)(28,47)(29,31)(30,45)(35,48)(36,38)(37,49)(39,41)(43,46)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2194, #17188281, #17188291, …
maximal subgroup of	C₂×C₁₇×#2194, C₁₇×#33538, C₁₇×#33539, …
maximal normal subgroup of	C₂×C₁₇×#2194, C₁₇×#33538, C₁₇×#33539, …
maximal quotient of	C₁₇×#12111, C₁₇×#12113, C₁₇×#12167, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 926);