C₂×C₅×C₉₇⋊C₃ #15668564

order	2910
isoclinism	isoclinic class of C₉₇⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₅×C₉₇⋊C₃
unambiguous semidirect product	(C₂×C₉₇)⋊(C₃×C₅)
unambiguous semidirect product	(C₂×C₅×C₉₇)⋊C₃

Splittings

Fitting, socle, Hall	C₂×C₅×C₉₇ ⋊ C₃
derived, Sylow	C₉₇ ⋊ C₂×C₃×C₅
Hall	C₅×C₉₇ ⋊ C₂×C₃
Hall	C₂×C₉₇ ⋊ C₃×C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	C₉₇⋊C₃
commutator, cosocle, hypocenter	C₉₇	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₉₇	C₃
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₂×C₅

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 104
transitive degree	μ_t(G) = 970

A minimal faithful permutation representation — 2 generators on 104 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₅×C₉₇⋊C₃, C₅×D₅×C₉₇⋊C₃, C₂×C₅²×C₉₇⋊C₃, …
maximal normal subgroup of	C₂×C₂₅×C₉₇⋊C₃, C₂×C₅²×C₉₇⋊C₃, C₂×C₅×C₇×C₉₇⋊C₃, …
maximal quotient of	C₂×C₂₅×C₉₇⋊C₃, C₅×D₅×C₉₇⋊C₃, C₂×C₅²×C₉₇⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2910, 2);

C2×C5×C97⋊C3 #15668564