C₂×#23761370 #34198030

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×#23761370

Splittings

Sylow

C₇₉ ⋊ C₂×#1334

Subgroups

	subgroup	G/H
center	C₂³	#14579082
commutator	C₈×C₇₉	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₇₉
Fitting	C₂×C₄×Q₁₆×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	#102
cosocle	C₄×C₈×C₇₉	C₂³
hypercenter	C₂×C₄×Q₁₆	D₇₉
hypocenter	C₇₉	C₂×#1334
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×Q₁₆

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 105
transitive degree	μ_t(G) = 20224

A minimal faithful permutation representation — 3 generators on 105 points:

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

Conjugacy classes & character table

2248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 79329);

C2×#23761370 #34198030