C₁₇×#2094 #14525100

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2094

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

290 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 108 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)(22,23,25,27)(24,28,29,26)(30,31,34,35,33,37,32,36);(18,19)(20,21)(22,24,25,29)(23,26,27,28)(31,35)(32,34)(36,37);(19,21)(31,35)(32,34)(36,37)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921930, #16923581, #16923585, …
maximal subgroup of	C₁₇×#7435, C₁₇×#7822, C₁₇×#7823, …
maximal normal subgroup of	C₁₇×#7435, C₁₇×#7822, C₁₇×#7823, …
maximal quotient of	C₁₇×#10661, C₁₇×#10666, C₁₇×#10672, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 826);