C₂×C₅×D₉₆₃ #34064093

order	19260
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₉₆₃
unambiguous semidirect product	(C₂×C₉)⋊(C₅×D₁₀₇)
unambiguous semidirect product	(C₂×C₁₀₇)⋊(C₅×D₉)

Splittings

Fitting	C₂×C₅×C₉×C₁₀₇ ⋊ C₂
derived, Hall	C₉×C₁₀₇ ⋊ C₂²×C₅
Hall	C₅×C₉×C₁₀₇ ⋊ C₂²
Hall	C₅×C₁₀₇ ⋊ C₂×D₉
Sylow	C₁₀₇ ⋊ C₂×C₅×D₉
Hall	C₅×C₉ ⋊ C₂×D₁₀₇
Sylow	C₉ ⋊ C₂×C₅×D₁₀₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	D₉₆₃
commutator, cosocle, hypocenter	C₉×C₁₀₇	C₂²×C₅
Frattini	C₃	C₂×C₅×D₃₂₁
Fitting	C₂×C₅×C₉×C₁₀₇	C₂
socle	C₂×C₃×C₅×C₁₀₇	D₃
LCS	G ▷ C₉×C₁₀₇
UCS	C₁ ◁ C₂×C₅

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 123
transitive degree	μ_t(G) = 9630

A minimal faithful permutation representation — 2 generators on 123 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)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(109,111)(110,114)(112,113)(115,116)(117,118,119,120,121);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(108,116,111,114,113,112,110,109,115)(122,123)

Conjugacy classes & character table

4830 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19260, 24);

C2×C5×D963 #34064093