C₁₇×#3259 #14526265

order	2176
nilpotency class	3
isoclinism	isoclinic class of #3198
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#3259

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₁₇×#117 ◁ G

370 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 41
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 4 generators on 41 points:

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946799, #16946816, #16946833, …
maximal subgroup of	C₁₇×#12164, C₁₇×#12167, C₁₇×#12170, …
maximal normal subgroup of	C₁₇×#12164, C₁₇×#12167, C₁₇×#12170, …
maximal quotient of	C₁₇×#21897, C₁₇×#21968, C₁₇×#22126, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1991);