C₁₇×#1968 #14524974

order	2176
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#1968

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

348 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 136 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)(19,21)(22,23,24,25)(27,32)(28,33)(29,30);(18,19,20,21)(23,25)(26,27,29,32,31,33,30,28);(26,28,30,33,31,32,29,27)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1968, #17038142, #17038178, …
maximal subgroup of	C₂×C₁₇×#1968, C₁₇×#21224, C₁₇×#21229, …
maximal normal subgroup of	C₂×C₁₇×#1968, C₁₇×#21224, C₁₇×#21229, …
maximal quotient of	C₁₇×#9655, C₁₇×#9661, C₁₇×#9717, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 700);