C₁₇×#1438 #14524444

order	2176
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₁₇×#1438

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₇	C₂³
commutator	C₂³	C₂²×C₄×C₁₇
Frattini, cosocle	C₂⁴	C₂³×C₁₇
prime radical	C₂³×D₄×C₁₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ G

1168 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 248 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)(30,31,32,33);(19,21)(23,25)(31,33);(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921070, #16921596, #16921603, …
maximal subgroup of	C₁₇×#7103, C₁₇×#7304, C₁₇×#7307, …
maximal normal subgroup of	C₁₇×#7103, C₁₇×#7304, C₁₇×#7307, …
maximal quotient of	C₁₇×#7555, C₁₇×#7557, C₁₇×#10964, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 170);