C₁₇×#2819 #14525825

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂×C₄³

Aliases

direct product

C₁₇×#2819

Subgroups

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

580 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 184 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)(22,23,25,27)(24,26,28,29)(30,31,34,33)(32,35,36,37);(19,21)(24,28)(26,29)(31,33)(32,36);(18,19)(20,21)(22,23)(24,26)(25,27)(28,29)(30,32)(31,35)(33,37)(34,36);(22,24)(23,26)(25,28)(27,29)(30,33,34,31)(32,35,36,37)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16935603, #16935621, #16935648, …
maximal subgroup of	C₁₇×#10078, C₁₇×#10081, C₁₇×#10085, …
maximal normal subgroup of	C₁₇×#10078, C₁₇×#10081, C₁₇×#10085, …
maximal quotient of	C₁₇×#14623, C₁₇×#14625, C₁₇×#14632, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1551);