#1401×D₇₉ #34208474

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂³

Aliases

direct product

#1401×D₇₉

Splittings

Fitting	C₇₉×#1401 ⋊ C₂
Sylow	C₇₉ ⋊ C₂×#1401

Subgroups

	subgroup	G/H
center	C₁₆	D₄×D₇₉
commutator	C₄×C₇₉	C₂²×C₁₆
Frattini	C₂×C₁₆	C₂²×D₇₉
Fitting	C₇₉×#1401	C₂
socle	C₂×C₇₉	C₂×C₂²⋊C₁₆
prime radical	#41×D₇₉	C₈
cosocle	C₂×C₁₆×C₇₉	C₂³
hypercenter	#1401	D₇₉
hypocenter	C₇₉	C₂×#1401
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #1401

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 143
transitive degree	μ_t(G) = 5056

A minimal faithful permutation representation — 3 generators on 143 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)(81,88)(83,99)(84,102)(85,97)(86,95)(87,98)(89,112)(90,115)(91,110)(92,94)(93,111)(96,105)(100,123)(101,127)(103,130)(104,108)(106,124)(107,126)(109,118)(113,121)(114,136)(116,138)(117,129)(119,122)(120,135)(125,132)(128,142)(131,133)(134,140)(137,141)(139,143);(80,81,84,90,85,91,103,116,86,92,104,117,106,119,131,139,87,93,105,118,107,120,132,140,83,89,100,113,101,114,128,137)(82,94,96,121,97,122,125,141,95,111,123,115,124,135,142,138,98,112,102,129,126,136,130,143,99,88,108,109,127,110,133,134)

Conjugacy classes & character table

2296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 89773);

#1401×D79 #34208474