C₁₇×#1440 #14524446

order	2176
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#1440

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₇	C₂³
commutator	C₂³	C₂²×C₄×C₁₇
Frattini, cosocle	C₂⁴	C₂³×C₁₇
prime radical	C₂⁵×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ G

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

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 216 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)(23,25)(26,27,28,29)(30,31,33,32);(19,21)(23,25)(31,32);(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,32,33,31)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921641, #16926898, D₁₇×#1440, …
maximal subgroup of	C₁₇×#7324, C₁₇×#8535, C₂×C₁₇×#1440, …
maximal normal subgroup of	C₁₇×#7324, C₁₇×#8535, C₂×C₁₇×#1440, …
maximal quotient of	C₁₇×#7555, C₁₇×#7556, C₁₇×#11147, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 172);