C₁₇×#2379 #14525385

order	2176
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₇×#2379

Subgroups

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

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

normal subgroups only

This group has 520 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) = 37
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 4 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(23,26)(24,28)(30,31)(32,36)(33,34)(35,37);(23,26)(27,29)(31,34)(32,37);(22,23,25,26)(24,27,28,29)(30,31)(32,35)(33,34)(36,37);(22,24)(23,27)(25,28)(26,29)(30,32,33,37)(31,35,34,36)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16928679, #16928685, #16928703, …
maximal subgroup of	C₁₇×#8910, C₁₇×#8911, C₁₇×#8914, …
maximal normal subgroup of	C₁₇×#8910, C₁₇×#8911, C₁₇×#8914, …
maximal quotient of	C₁₇×#13829, C₁₇×#13831, C₁₇×#13832, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1111);