C₁₇×#1717 #14524723

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₇×#1717

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₁₇×#493	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

208 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 33
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1717, #17022092, #17022134, …
maximal subgroup of	C₂×C₁₇×#1717, C₁₇×#19613, C₁₇×#19619, …
maximal normal subgroup of	C₂×C₁₇×#1717, C₁₇×#19613, C₁₇×#19619, …
maximal quotient of	C₁₇×#8821, C₁₇×#9827, C₁₇×#9829, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 449);