#1389×D₇₉ #34203202

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

#1389×D₇₉

Splittings

Fitting	C₇₉×#1389 ⋊ C₂
Sylow	C₇₉ ⋊ C₂×#1389

Subgroups

	subgroup	G/H
center	C₄	#102×D₇₉
commutator	C₈×C₇₉	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#1389	C₂
socle	C₂×C₇₉	C₂×#340
prime radical	C₂³×D₇₉	SD₁₆
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	#1389	D₇₉
hypocenter	C₇₉	C₂×#1389
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1389

570 conjugacy classes of subgroups.

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)(80,82,83,94,84,93,98,109,86,96,100,92,85,95,99,102)(81,87,88,104,101,107,111,108,90,105,106,91,89,103,97,110);(80,81,84,89,86,90,85,101)(82,91,93,108,96,104,95,110)(83,97,98,106,100,111,99,88)(87,102,103,94,105,109,107,92)

Conjugacy classes & character table

1312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 84501);

#1389×D79 #34203202