C₂×C₄₉×D₆₇ #27190067

order	13132
isoclinism	isoclinic class of D₆₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₄₉×D₆₇
unambiguous semidirect product	C₆₇⋊(C₂²×C₄₉)
unambiguous semidirect product	(C₂×C₆₇)⋊(C₂×C₄₉)

Splittings

Fitting	C₂×C₄₉×C₆₇ ⋊ C₂
derived, Sylow	C₆₇ ⋊ C₂²×C₄₉
Hall	C₄₉×C₆₇ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₉	D₆₇
commutator, hypocenter	C₆₇	C₂²×C₄₉
Frattini	C₇	C₂×C₇×D₆₇
Fitting	C₂×C₄₉×C₆₇	C₂
socle	C₂×C₇×C₆₇	C₂×C₇
prime radical	C₂×C₇×D₆₇	C₇
cosocle	C₇×C₆₇	C₂²×C₇
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₂×C₄₉

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 118
transitive degree	μ_t(G) = 6566

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

Conjugacy classes & character table

3430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13132, 7);

C2×C49×D67 #27190067