C₁₇×#2164 #14525170

order	2176
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#2164

Subgroups

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

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

normal subgroups only

This group has 138 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) = 57
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27,29,33,30,34,39,45,31,35,40,46,41,47,51,55)(28,32,37,43,38,44,50,54,36,42,48,52,49,53,56,57);(19,22)(23,25)(26,28)(27,32)(29,37)(30,38)(31,36)(33,43)(34,44)(35,42)(39,50)(40,48)(41,49)(45,54)(46,52)(47,53)(51,56)(55,57);(18,20,21,24)(19,23,22,25)(28,36)(32,42)(37,48)(38,49)(43,52)(44,53)(50,56)(54,57)

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2164, #17187407, #17187414, …
maximal subgroup of	C₂×C₁₇×#2164, C₁₇×#33419, C₁₇×#33420, …
maximal normal subgroup of	C₂×C₁₇×#2164, C₁₇×#33419, C₁₇×#33420, …
maximal quotient of	C₁₇×#12592, C₁₇×#12600, C₁₇×#12654, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 896);