#1423×D₇₉ #34208763

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

direct product

#1423×D₇₉

Splittings

Fitting	C₇₉×#1423 ⋊ C₂
Sylow	C₇₉ ⋊ C₂×#1423

Subgroups

	subgroup	G/H
center	C₂²	D₁₆×D₇₉
commutator	C₁₆×C₇₉	C₂²×C₄
Frattini	C₂×C₁₆	C₂²×D₇₉
Fitting	C₇₉×#1423	C₂
socle	C₂²×C₇₉	C₂×D₁₆
prime radical	C₂²×D₇₉	D₁₆
cosocle	C₂×C₁₆×C₇₉	C₂³
hypercenter	#1423	D₇₉
hypocenter	C₇₉	C₂×#1423
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1423

206 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 91 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) = 10112

A minimal faithful permutation representation — 3 generators on 115 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)(84,85,91,101,87,92,104,110,98,108,112,115,111,113,97,103,89,94,106,114,99,109,96,102,88,93,105,107,95,100,86,90);(80,81,82,83)(85,90)(86,91)(87,95)(88,98)(92,107)(93,110)(94,103)(96,112)(97,106)(99,111)(100,101)(102,108)(104,105)(109,115)(113,114)

Conjugacy classes & character table

1558 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 90062);