C₁₇×#2175 #14525181

order	2176
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2175

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₈
commutator	C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₂×D₈×C₁₇	C₂²
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

160 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 80 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 — 3 generators on 37 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946198, #16946276, #16946297, …
maximal subgroup of	C₁₇×#12065, C₁₇×#12077, C₁₇×#12080, …
maximal normal subgroup of	C₁₇×#12065, C₁₇×#12077, C₁₇×#12080, …
maximal quotient of	C₁₇×#12043, C₁₇×#12074, C₁₇×#12075, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 907);