C₁₇×#2192 #14525198

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2192
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2192

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#447
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#131 ◁ G

220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,31)(21,35)(22,29)(23,28)(24,30)(25,32)(26,33)(27,38)(34,46)(36,47)(37,41)(39,45)(40,44)(42,49)(43,48);(18,20)(19,25)(21,36)(22,33)(23,40)(24,34)(26,41)(27,44)(28,42)(29,47)(30,43)(31,35)(32,38)(37,48)(39,49)(45,46);(18,20)(19,26)(21,32)(22,40)(23,33)(24,34)(25,41)(27,43)(28,46)(29,31)(30,44)(35,47)(36,38)(37,49)(39,48)(42,45)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2192, #17188275, #17188286, …
maximal subgroup of	C₂×C₁₇×#2192, C₁₇×#33538, C₁₇×#33539, …
maximal normal subgroup of	C₂×C₁₇×#2192, C₁₇×#33538, C₁₇×#33539, …
maximal quotient of	C₁₇×#12108, C₁₇×#12110, C₁₇×#12164, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 924);