C₂×C₇₉×D₄₁ #27188361

order	12956
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇₉×D₄₁
unambiguous semidirect product	C₄₁⋊(C₂²×C₇₉)
unambiguous semidirect product	(C₂×C₄₁)⋊(C₂×C₇₉)

Splittings

Fitting, socle	C₂×C₄₁×C₇₉ ⋊ C₂
derived, Sylow	C₄₁ ⋊ C₂²×C₇₉
Hall	C₄₁×C₇₉ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇₉	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂²×C₇₉
Frattini	C₁	G
Fitting, socle	C₂×C₄₁×C₇₉	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₇₉

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 122
transitive degree	μ_t(G) = 6478

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

Conjugacy classes & character table

3476 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12956, 10);

C2×C79×D41 #27188361