C₈₃×#7398 #35235222

order	21248
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₈₃×#7398

Subgroups

	subgroup	G/H
center, socle	C₂×C₈₃	#1343
commutator	C₂²×C₈	C₂×C₄×C₈₃
Frattini, cosocle	#408	C₂²×C₈₃
prime radical	C₈₃×#2018	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₃ ◁ C₂×C₄×C₈₃ ◁ C₂²×C₄×C₈₃ ◁ #408×C₈₃ ◁ G

258 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 42 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) = 115
transitive degree	μ_t(G) = 2656

A minimal faithful permutation representation — 2 generators on 115 points:

(1,2,4,9)(3,8,14,25)(5,10,19,27)(6,11,18,26)(7,20,21,12)(13,24,16,29)(15,22,17,30)(23,31,32,28)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(2,7)(3,12)(4,16)(5,13)(8,10)(9,25)(11,23)(15,28)(18,19)(20,31)(21,29)(22,24)(26,30)(27,32)

Conjugacy classes & character table

2075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 386);