#1426×D₇₉ #34208784

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#1426×D₇₉

Splittings

Fitting	C₇₉×#1426 ⋊ C₂
Sylow	C₇₉ ⋊ C₂×#1426

Subgroups

	subgroup	G/H
center	C₂	#367×D₇₉
commutator	C₁₆×C₇₉	C₂²×C₄
Frattini	C₂×C₁₆	C₂²×D₇₉
Fitting	C₇₉×#1426	C₂
socle	C₂×C₇₉	C₂×#367
prime radical	C₂²×D₇₉	SD₃₂
cosocle	C₂×C₁₆×C₇₉	C₂³
hypercenter	#1426	D₇₉
hypocenter	C₇₉	C₂×#1426
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1426

190 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 81 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) = 111
transitive degree	μ_t(G) = 2528

A minimal faithful permutation representation — 3 generators on 111 points:

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

Conjugacy classes & character table

1066 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 90083);