C₁₇×#2858 #14525864

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₁₇×#2858

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#127	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

752 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 264 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 — 4 generators on 33 points:

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

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16922680, #16922772, #16922864, …
maximal subgroup of	C₁₇×#7659, C₁₇×#7679, C₁₇×#7699, …
maximal normal subgroup of	C₁₇×#7659, C₁₇×#7679, C₁₇×#7699, …
maximal quotient of	C₁₇×#14687, C₁₇×#14700, C₁₇×#14708, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1590);