C₁₇×#2848 #14525854

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#2848

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂⁵×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

1068 conjugacy classes of subgroups; only the 288 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 288 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) = 33
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(23,25)(26,27,29,31)(28,32,33,30);(26,28,29,33)(27,30,31,32);(22,23)(24,25);(18,19)(20,21)(22,23)(24,25)(26,27)(28,30)(29,31)(32,33)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16929880, #16929900, #16930040, …
maximal subgroup of	C₁₇×#9111, C₁₇×#9115, C₁₇×#9143, …
maximal normal subgroup of	C₁₇×#9111, C₁₇×#9115, C₁₇×#9143, …
maximal quotient of	C₁₇×#14680, C₁₇×#14693, C₁₇×#14695, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1580);