C₁₇×#2853 #14525859

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×#2853

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

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

normal subgroups only

This group has 582 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)(23,25)(24,28)(31,34)(32,36);(22,23,26,25)(24,27,28,29)(30,31)(32,35)(33,34)(36,37);(22,24)(23,27)(25,29)(26,28);(18,19)(20,21)(22,25,26,23)(24,29,28,27)(30,32,33,36)(31,35,34,37)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#17067564, #17068188, #17206890, …
maximal subgroup of	C₁₇×#24057, C₁₇×#24113, C₁₇×#34983, …
maximal normal subgroup of	C₁₇×#24057, C₁₇×#24113, C₁₇×#34983, …
maximal quotient of	C₁₇×#14684, C₁₇×#14695, C₁₇×#14696, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1585);