C₂×C₅×C₃⋊D₂₆₇ #30630899

order	16020
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₅×C₃⋊D₂₆₇
unambiguous semidirect product	(C₂×C₃)⋊(C₅×D₂₆₇)
unambiguous semidirect product	(C₂×C₈₉)⋊(C₅×C₃⋊D₃)

Splittings

Fitting, socle	C₂×C₃²×C₅×C₈₉ ⋊ C₂
derived, Hall	C₃²×C₈₉ ⋊ C₂²×C₅
Hall	C₃²×C₅×C₈₉ ⋊ C₂²
Hall	C₅×C₈₉ ⋊ C₂×C₃⋊D₃
Sylow	C₈₉ ⋊ C₂×C₅×C₃⋊D₃
Hall	C₃²×C₅ ⋊ C₂×D₈₉
Sylow	C₃² ⋊ C₂×C₅×D₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊D₂₆₇
commutator, cosocle, hypocenter	C₃²×C₈₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₈₉	C₂
LCS	G ▷ C₃²×C₈₉
UCS	C₁ ◁ C₂×C₅

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 102
transitive degree	μ_t(G) = 8010

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

Conjugacy classes & character table

4020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16020, 104);

C2×C5×C3⋊D267 #30630899