C₁₇×#2734 #14525740

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2734

Subgroups

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

456 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 224 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) = 2176

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)(23,24)(27,28)(30,31,34,36)(32,33,37,35);(19,21)(22,23,26,24)(25,28,29,27)(30,32,34,37)(31,35,36,33);(18,19)(20,21)(22,24,26,23)(25,28,29,27);(22,25)(23,27)(24,28)(26,29)(30,33,34,35)(31,32,36,37)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16923064, #16923152, #16923208, …
maximal subgroup of	C₁₇×#7741, C₁₇×#7757, C₁₇×#7766, …
maximal normal subgroup of	C₁₇×#7741, C₁₇×#7757, C₁₇×#7766, …
maximal quotient of	C₁₇×#14406, C₁₇×#14441, C₁₇×#14450, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1466);