C₂₉×D₂₁₃ #27136402

order	12354
isoclinism	isoclinic class of D₂₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×D₂₁₃
unambiguous semidirect product	C₃⋊(C₂₉×D₇₁)
unambiguous semidirect product	C₇₁⋊(D₃×C₂₉)

Splittings

Fitting, socle, Hall	C₃×C₂₉×C₇₁ ⋊ C₂
derived, Hall	C₃×C₇₁ ⋊ C₂×C₂₉
Hall	C₂₉×C₇₁ ⋊ D₃
Hall	C₃×C₂₉ ⋊ D₇₁
Sylow	C₇₁ ⋊ D₃×C₂₉
Sylow	C₃ ⋊ C₂₉×D₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	D₂₁₃
commutator, cosocle, hypocenter	C₃×C₇₁	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₇₁	C₂
LCS	G ▷ C₃×C₇₁
UCS	C₁ ◁ C₂₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 103
transitive degree	μ_t(G) = 6177

A minimal faithful permutation representation — 2 generators on 103 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)(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);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(72,73,74)

Conjugacy classes & character table

3132 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×C₂₉×D₇₁, D₂₉×D₂₁₃, D₈₇⋊D₇₁, …
maximal normal subgroup of	D₃×C₂₉×D₇₁, D₂₉×D₂₁₃, D₈₇⋊D₇₁, …
maximal quotient of	C₂₉×Dic₂₁₃, C₂×C₂₉×D₂₁₃, C₂₉×D₆₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12354, 6);

C29×D213 #27136402