C₁₇×#3415 #14526421

order	2176
nilpotency class	4
isoclinism	isoclinic class of #3415
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#3415

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	C₂²×D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₁₇
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ #41×C₁₇ ◁ C₁₇×#131 ◁ G

370 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 180 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 — 4 generators on 49 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16955008, #16955022, #17191070, …
maximal subgroup of	C₁₇×#13669, C₁₇×#13671, C₁₇×#33854, …
maximal normal subgroup of	C₁₇×#13669, C₁₇×#13671, C₁₇×#33854, …
maximal quotient of	C₁₇×#33381, C₁₇×#33410, C₁₇×#33454, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2147);