C₁₇×#2215 #14525221

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2215

Subgroups

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

174 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 68 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)(20,21)(23,27)(24,28)(25,31)(29,37)(30,35)(32,36)(33,34);(22,23,28,34,25,29,32,35,26,30,36,37,31,33,24,27);(19,21)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921879, #16921885, #16954962, …
maximal subgroup of	C₁₇×#7418, C₁₇×#7420, C₁₇×#13661, …
maximal normal subgroup of	C₁₇×#7418, C₁₇×#7420, C₁₇×#13661, …
maximal quotient of	C₁₇×#12430, C₁₇×#12439, C₁₇×#12451, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 947);