D₄₉×D₆₇ #27190066

order	13132
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₄₉×D₆₇
unambiguous semidirect product	(C₆₇×D₄₉)⋊C₂
unambiguous semidirect product	(C₄₉×D₆₇)⋊C₂
unambiguous semidirect product	D₃₂₈₃⋊C₂

Splittings

Fitting, derived, Hall	C₄₉×C₆₇ ⋊ C₂²
Sylow	C₆₇ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×D₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₄₉×C₆₇	C₂²
Frattini	C₇	D₇×D₆₇
socle	C₇×C₆₇	C₂×D₇
LCS	G ▷ C₄₉×C₆₇
UCS	C₁

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 116
transitive degree	μ_t(G) = 3283

A minimal faithful permutation representation — 2 generators on 116 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)(68,73,91,112,111,90,71,70,81,104,115,101,77,76,75,93,114,109,87,86,85,84,106,107,99,88,98,97,96,95,94,78,100,108,105,83,82,72,89,110,113,92,74,69,79,102,116,103,80);(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)(69,71)(70,74)(72,77)(73,80)(75,83)(76,82)(78,87)(79,90)(81,92)(84,96)(85,95)(86,94)(88,99)(89,101)(91,103)(93,105)(97,106)(98,107)(100,109)(102,111)(104,113)(108,114)(110,115)(112,116)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13132, 6);

D49×D67 #27190066