C₁₇×#2193 #14525199

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

Aliases

direct product

C₁₇×#2193

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

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

normal subgroups only

This group has 210 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)(19,25)(20,29)(21,32)(22,23)(26,40)(27,44)(28,39)(30,46)(31,36)(33,37)(34,35)(38,41)(42,49)(43,47);(18,19)(20,26)(21,33)(22,27)(23,37)(24,28)(25,32)(29,41)(30,47)(31,43)(34,39)(35,44)(36,42)(38,45)(40,46)(48,49);(18,20,24,31)(19,26,28,43)(21,30,35,46)(22,36,23,29)(25,38,39,49)(27,42,37,41)(32,45,34,48)(33,47,44,40)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2193, #17188277, #17188295, …
maximal subgroup of	C₂×C₁₇×#2193, C₁₇×#33538, C₁₇×#33540, …
maximal normal subgroup of	C₂×C₁₇×#2193, C₁₇×#33538, C₁₇×#33540, …
maximal quotient of	C₁₇×#12109, C₁₇×#12110, C₁₇×#12165, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 925);