C₂×#23761467 #34199830

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

Aliases

direct product

C₂×#23761467

Splittings

Sylow

C₇₉ ⋊ C₂×#1369

Subgroups

	subgroup	G/H
center	C₂×C₄	#14579092
commutator	C₈×C₇₉	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₇₉
Fitting	C₂×#364×C₇₉	C₂
socle	C₂²×C₇₉	#334
prime radical	C₂³×C₇₉	#108
cosocle	C₄×C₈×C₇₉	C₂³
hypercenter	C₂×#364	D₇₉
hypocenter	C₇₉	C₂×#1369
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#364

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 113
transitive degree	μ_t(G) = 5056

A minimal faithful permutation representation — 3 generators on 113 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)(82,84,85,96,87,98,102,97,89,100,103,111,88,99,86,104)(83,90,91,95,93,106,101,110,94,107,92,108,105,113,109,112);(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)(82,83,86,92,88,93,103,109,89,94,102,91,87,105,85,101)(84,95,97,106,99,110,96,107,100,108,104,113,98,112,111,90);(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, 81129);

C2×#23761467 #34199830