C₁₇×#1929 #14524935

order	2176
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#1929

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle	C₂²×C₁₇	C₄×D₄
prime radical	C₂×#41×C₁₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

224 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 544

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1929, #17036827, #17036835, …
maximal subgroup of	C₂×C₁₇×#1929, C₁₇×#21070, C₁₇×#21071, …
maximal normal subgroup of	C₂×C₁₇×#1929, C₁₇×#21070, C₁₇×#21071, …
maximal quotient of	C₁₇×#9541, C₁₇×#9542, C₁₇×#9543, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 661);