C₁₇×#2861 #14525867

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#2861

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

524 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 216 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)(19,21)(23,26)(27,29)(31,33)(35,36);(22,23)(24,27)(25,26)(28,29)(30,31,34,33)(32,35,37,36);(18,19,20,21)(22,23)(24,27)(25,26)(28,29)(30,32,34,37)(31,35,33,36);(22,24,25,28)(23,27,26,29)(30,33,34,31)(32,36,37,35)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16922666, #16922758, #16922850, …
maximal subgroup of	C₁₇×#7656, C₁₇×#7676, C₁₇×#7696, …
maximal normal subgroup of	C₁₇×#7656, C₁₇×#7676, C₁₇×#7696, …
maximal quotient of	C₁₇×#14689, C₁₇×#14700, C₁₇×#14701, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1593);